West Indies v England: Essential win lifts World Cup gloom

Alastair Cook and Gary Ballance scored 293 runs between them in the match

The reaction of England's players after they wrapped up victory in the second Test against West Indies said it all.

It was almost reminiscent of the scenes after an Ashes win: pulling up stumps, hugging each other, running to celebrate with the spectators who had come so far to support them.

I could feel the joy and relief from where I was sitting three floors up in the commentary box.

This was an important win for Alastair Cook's men. It was absolutely essential to change the mood around the team after their disastrous performance at the World Cup.

They took a real hiding in Australia and New Zealand and that clouded a lot of opinion. Their recent Test record isn't actually that bad, but they hadn't managed an away win in this format of the game since beating India at Kolkata in December 2012.

So to get over the line in a gruelling Test match like this will give the team a huge amount of satisfaction. Victories like this, achieved on a slow, lifeless pitch, are often the best, because they require moments of real brilliance.

James Anderson claimed four wickets, a catch and a run-out in the morning session

That was provided by James Anderson in the morning session. To have a hand in all six wickets taken was simply remarkable - it was one of the outstanding individual performances I've seen from an England cricketer.

It was started by a magnificent delivery to dismiss the West Indies centurion Kraigg Brathwaite. To get the ball to kick on an unresponsive pitch like this doesn't happen by accident: it's class, it's rhythm, it's a snap of the wrist.

He had no right to produce a ball like that on this pitch, but that is what sets a bowler of Anderson's calibre apart.

There are plenty of reasons for optimism heading into the third Test in Barbados, where England will be determined to go 2-0 up in the final game of the series, but there are still one or two areas that need to be looked at.

I remain concerned about Jonathan Trott at the top of the order. He will be under renewed pressure after his third cheap dismissal of the series.

I feel really sorry for him after all he's been through. He's batting in an unfamiliar position, which is very demanding.

I'm sure he jumped at the chance to open the batting, but one of the most important aspects of playing at the top of the order is the importance of creating calm.

You've got to look composed, to send a message to your team-mates and your opponents, and I'm afraid I don't see that from Trott. Anyone can make a duck, but it's how you make it - Trott looked very discomfited and could have got out to any of the three balls he faced.

I would bring in Yorkshire's Adam Lyth for Trott for the Barbados Test. He's a bit more of a free scorer, which I think is important - you don't necessarily want someone like Chris Gayle at the top of the order, but given that Cook and Gary Ballance are both naturally defensive I don't think it would do any harm to have someone who looks to put bat to ball.

Depending on conditions in Barbados, I would also like to see England pick leg-spinner Adil Rashid for his variation, or seamer Liam Plunkett for his pace.

It may seem harsh to change a winning side, but I just believe that's the right way for England looking forward to the series against New Zealand and Australia this summer.

Jonathan Agnew was speaking to BBC Sport's James Gheerbrant.