And watch out for the Test Match Special podcast available later here.
Catch you on Friday. Go well.
Post update
More from Jason Roy on his partnership with Joe Root: "We batted well together, rotated the strike very well and it was really impressive to see him carry on to take us home.
"We just keep striving for better and better. We've won today but we'll keep our feet on the floor and we need to work hard again on Friday."
Post update
Player of the match Jason Roy, who hit 123: "It was a nice surface to bat on, although it was quite daunting at the start. But me and Jonny got off to a great start and carried on from there.
"Thanks for reminding about dropping Chris Gayle on nine. I'm still in deficit so owe the team some more runs in the series.
"Of course that's in the back of your mind, you want to step up and do something for the team."
Post update
They've found Jason Roy.
He's missed his chance to pose with the big cheque but he's going to have a word with Daren Ganga to end the presentation...
Post update
England captain Eoin Morgan on Jason Roy and Joe Root's contrasting styles:"It's a huge asset, particularly when they bat together - they really complemented each other. The styles in which they play make it very difficult for the opposition."
Post update
England captain Eoin Morgan on the most pleasing aspect of victory: "The calm nature in which we came back with the ball.
"West Indies looked like posting up to 400, and the way in which we approached the last 10 overs hauled them back. Adil was a huge part in pegging the West Indies back.
"The way we went about the chase - it felt like a 330 chase rather than a 360. You can't look past the opening partnership. For Jason Roy to play such a commanding role at the top of the order set us up beautifully."
'We're improving constantly'
England captain Eoin Morgan: "We're delighted. I'd like to think we're improving constantly as we go along, which is a good place to be in for the World Cup."
Post update
More from Jason Holder: "We were not up to scratch in the field with our energy and body language. We need to pull up our socks with our fielding and if we do that, then we can create some energy for the bowlers.
"The bowlers did create the chances but we didn't hold them. You can't put dangerous players like that down."
Post update
Windies captain Jason Holder on Chris Gayle's century: "I love the way he went about his innings. He took his time, gave himself a chance in the middle and then went deep for us.
"It's good to see him out there playing the way he is. Hopefully he can carry on giving more of that in the rest of the series."
Post update
West Indies captain Jason Holder: "Credit to our batters, they batted well and it was a remarkable effort to get 360.
"We were in the game but we didn't bowl as well as we could and let ourselves down in the field."
Post update
England opener Jason Roy is named player of the match for his stellar 123 off 85 balls.
Roy isn't at the presentation though so Eoin Morgan gets the big cheque and the handshake.
Get Involved
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James'll Do It: After decades of watching England labour to get runs in ODIs, this team is a joy to watch.
Post update
So England have just completed their highest ever ODI run chase and the fourth-highest in ODI history.
And it looked pretty inevitable from the end of the first powerplay.
And Jos Buttler only faced one ball (which he hit for four, natch).
Mad.
Get Involved
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Joe Golden: Why can't we do that in the Tests?
Post update
Can't focus on Chris Gayle's innings too much though - West Indies did not field or bowl well at all.
They were four or five dropped catches and several misfields.
The bowling attack was clearly missing the injured Kemar Roach, with Oshane Thomas a fine prospect but inexperienced and their spinners were unable to offer much control.
Jason Holder led from the front again with 2-63 but he needs more help.
Get Involved
#bbccricket
Mark Welburn: Not often you can look at a player scoring a ton and say they cost their team the game. But Gayle's 61 dot balls were far too many.
Getty ImagesCopyright: Getty Images
Post update
Can you call a knock of 135 off 129 balls costly?
It seems strange but Chris Gayle's approach - peppering runs of dot balls with towering sixes - was shown up by England as somewhat outmoded.
Jason Roy and Eoin Morgan had much higher strike rates. And Joe Root scored his ton off fewer balls.
SMS Message: That's scary how easy England made that look. from Dominic
That's scary how easy England made that look.
Post update
West Indies hit 23 sixes - an ODI record.
England hit only six sixes.
But the tourists hit 37 fours to the hosts' 21 and ran much, much better.
We've become used to England achieving these feats in ODI cricket, but this was a really stunning victory. The calmness with which they went about it so impressive.
Live Reporting
Jack Skelton and Amy Lofthouse
All times stated are UK
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Latest PostFarewell
So England take a 1-0 lead in the five-match ODI series.
The second match is also at Barbados on Friday at 15:00 GMT. We look forward to you joining us again then.
For now, Amy Lofthouse's report of England's record-breaking win is here.
The scorecard is here.
And watch out for the Test Match Special podcast available later here.
Catch you on Friday. Go well.
Post update
More from Jason Roy on his partnership with Joe Root: "We batted well together, rotated the strike very well and it was really impressive to see him carry on to take us home.
"We just keep striving for better and better. We've won today but we'll keep our feet on the floor and we need to work hard again on Friday."
Post update
Player of the match Jason Roy, who hit 123: "It was a nice surface to bat on, although it was quite daunting at the start. But me and Jonny got off to a great start and carried on from there.
"Thanks for reminding about dropping Chris Gayle on nine. I'm still in deficit so owe the team some more runs in the series.
"Of course that's in the back of your mind, you want to step up and do something for the team."
Post update
They've found Jason Roy.
He's missed his chance to pose with the big cheque but he's going to have a word with Daren Ganga to end the presentation...
Post update
England captain Eoin Morgan on Jason Roy and Joe Root's contrasting styles:"It's a huge asset, particularly when they bat together - they really complemented each other. The styles in which they play make it very difficult for the opposition."
Post update
England captain Eoin Morgan on the most pleasing aspect of victory: "The calm nature in which we came back with the ball.
"West Indies looked like posting up to 400, and the way in which we approached the last 10 overs hauled them back. Adil was a huge part in pegging the West Indies back.
"The way we went about the chase - it felt like a 330 chase rather than a 360. You can't look past the opening partnership. For Jason Roy to play such a commanding role at the top of the order set us up beautifully."
'We're improving constantly'
England captain Eoin Morgan: "We're delighted. I'd like to think we're improving constantly as we go along, which is a good place to be in for the World Cup."
Post update
More from Jason Holder: "We were not up to scratch in the field with our energy and body language. We need to pull up our socks with our fielding and if we do that, then we can create some energy for the bowlers.
"The bowlers did create the chances but we didn't hold them. You can't put dangerous players like that down."
Post update
Windies captain Jason Holder on Chris Gayle's century: "I love the way he went about his innings. He took his time, gave himself a chance in the middle and then went deep for us.
"It's good to see him out there playing the way he is. Hopefully he can carry on giving more of that in the rest of the series."
Post update
West Indies captain Jason Holder: "Credit to our batters, they batted well and it was a remarkable effort to get 360.
"We were in the game but we didn't bowl as well as we could and let ourselves down in the field."
Post update
England opener Jason Roy is named player of the match for his stellar 123 off 85 balls.
Roy isn't at the presentation though so Eoin Morgan gets the big cheque and the handshake.
Get Involved
#bbccricket
James'll Do It: After decades of watching England labour to get runs in ODIs, this team is a joy to watch.
Post update
So England have just completed their highest ever ODI run chase and the fourth-highest in ODI history.
And it looked pretty inevitable from the end of the first powerplay.
And Jos Buttler only faced one ball (which he hit for four, natch).
Mad.
Get Involved
#bbccricket
Joe Golden: Why can't we do that in the Tests?
Post update
Can't focus on Chris Gayle's innings too much though - West Indies did not field or bowl well at all.
They were four or five dropped catches and several misfields.
The bowling attack was clearly missing the injured Kemar Roach, with Oshane Thomas a fine prospect but inexperienced and their spinners were unable to offer much control.
Jason Holder led from the front again with 2-63 but he needs more help.
Get Involved
#bbccricket
Mark Welburn: Not often you can look at a player scoring a ton and say they cost their team the game. But Gayle's 61 dot balls were far too many.
Post update
Can you call a knock of 135 off 129 balls costly?
It seems strange but Chris Gayle's approach - peppering runs of dot balls with towering sixes - was shown up by England as somewhat outmoded.
Jason Roy and Eoin Morgan had much higher strike rates. And Joe Root scored his ton off fewer balls.
Post update
Get Involved
Text 81111
Post update
West Indies hit 23 sixes - an ODI record.
England hit only six sixes.
But the tourists hit 37 fours to the hosts' 21 and ran much, much better.
We've become used to England achieving these feats in ODI cricket, but this was a really stunning victory. The calmness with which they went about it so impressive.