He was subsequently left out of the team for next month's West Indies tour, raising doubts over his availability for the trip to the UK.
But he told Indian newspaper Mid Day: "I think I will able to play the series in England.
"That's the reason why I stopped playing the Indian Premier League for Delhi Daredevils and rushed to London to get my shoulder operated.
"I will return to London after six weeks for a check-up. I should be fit in six to eight weeks.
"Going by the rehabilitation programme designed for me, I should be OK. I am already feeling the difference each day."
India's tour of England will see Duncan Fletcher, their new coach, take charge of team affairs for the first time since replacing the South African Gary Kirsten after this year's successful World Cup campaign.
Prior commitments mean the Zimbabwean will not be at the helm when India travel to the Caribbean, but he is set to take charge in preparation for the much-anticipated tour of England - a team he coached from 1999 until 2007.
India will play four Tests, a Twenty20 international and then five one-day matches in England between July and September.