Cook’s men briefly lost their place at the summit of the standings after a heavy defeat by South Africa in Southampton last week.
But they bounced back in London following wins by four and six wickets in the one-day internationals (ODIs) at The Oval and Lord’s respectively.
“It’s certainly not a bad thing,” Cook, who last week also became England’s Test captain after the retirement of Andrew Strauss, said of being number one.
“But I think we feel this side has its future ahead of it, rather than behind it,” explained the 27-year-old opening batsman. “We’re still striving to improve in all areas. We’ve only been together for a year or so.
“We’ve had some really good results, but certainly don’t feel like the number one side — like we did when we got there as a Test team,” Cook said.
“Clearly after what’s happened this summer, we could have let our heads go down — a bit of a case of ‘here we go again’,” said Cook.
“We admitted we didn’t get it right at the Ageas Bowl (in Southampton), and we’ve bounced back really well.
“We’ve still got a series to win, but I’m very proud of what we’ve done this weekend in back-to-back matches.”
Ian Bell, who was the man-of-the-match at Lord’s, replaced Kevin Pietersen as an opener after the South Africa-born batsman briefly retired from limited overs internationals. Pietersen has since rescinded that decision but finds himself in England exile over issues of “trust and mutual respect”.
But whatever the Test ramifications, Bell’s form means Pietersen has not been missed in one-dayers. “It was a classy knock again. I say that time and time again when you watch Belly play,” said Cook.
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