Victories at home to Estonia on Friday and away to Lithuania next Monday would give Roy Hodgson's side 10 wins out of 10 -- something no other country can emulate.
Sitting nine points ahead of Switzerland, they are already guaranteed to win the group.
"Hopefully we can go 10 undefeated," Arsenal's Walcott told a news conference. "It would be a great achievement to win 10 out of 10."
Manchester City goalkeeper Hart was more dismissive, however.
"It's two games away from happening and I don't see it as being that great an achievement unless we go on and do well at the finals," he said.
England have often sailed through their qualifying group for major tournaments but then failed when they got there.
"We were disappointed a couple of summers ago," Hart said of the last World Cup in Brazil when England finished bottom of their group after failing to win a game.
"But we've reacted in the right way," he added of the new campaign.
(Reporting by Steve Tongue; editing by Ken Ferris)
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