Lend Lease helped the Brits, no question, but not to win the Battle of Britain - the Hurricanes and Spitfires were entirely British designed, built and manned. Their radar networks were entirely of their own devising (and well ahead of anything America had at the time).
Britain could not have won the war without America. But they weren't losing when we came in, either. And there's no questioning their dedication or tenacity.
There's serious anti-Americanism in Britain, but these old vets aren't the ones to go after on that score - they know better than anyone what they owe to America, and unlike most of their younger compatriots, they put it on the line when it counted. I'd chalk it up to old resentments at that the Hollywoodization of their story - something even Americans can sympathize with.