Captain Michael Vaughan was happy with England's best performance of the World Cup group stage as they overcame Kenya.
Vaughan himself failed with the bat again in St Lucia
"When you come up against a potential banana skin you just want to get the basics done right," he said.
"We wanted to be very professional and that's exactly what we were - in all areas of the game.
"We're now going to the Super 8 and hopefully we can take the momentum of the last two victories and make sure we start well against Ireland."
Vaughan admitted it had been a difficult few days with the furore about a late night drinking session involving a group of England players being followed by the murder of Pakistan coach Bob Woolmer.
"It's been a tough week for everyone, but the players have focused well in practice and when you do that you tend to get good performances."
Vaughan praised his new ball bowlers, saying: "James Anderson made good use of the conditions, and Sajid Mahmood gave us something different as his slower balls deceived some of the batsmen."
The win was sealed by half centuries from Ed Joyce and Kevin Pietersen and Pietersen was also happy to progress to the next phase of the tournament.
Pietersen shared a century stand with opener Ed Joyce
"It's not been a good week for cricket, but for us to win by seven wickets was really good for the boys," admitted Pietersen, who hit 56 not out.
"But now we've got to play Ireland in Guyana next week, and we've got to keep the momentum going.
"We're adapting to the conditions, but we'll hopefully get back here [St Lucia] for the semi-finals."
Joyce was named Man of the Match for his 75 and he, in particular, is relishing the next match against an Irish side he used to play for before qualifying for England.
"It's going to be a pretty interesting game for me - I've played against them before in my first game [for England] but being an Irishman, it's always a strange one playing against them for England," he told BBC Sport.
"They'll bring a big crowd with them and it will be a good day. They [the Irish fans] travel with the right mentality, that they're going to have fun, and it puts a team under a lot less pressure if your supporters are going to have fun regardless of the result."
He added: "They've had some good results and put in some good performances. I think they need to get on top early and keep their foot on people's necks - that's their best method of winning.
"Hopefully, they'll cause a shock or two [in the Super 8s] but not against England."