How much help are the Americans giving them? The Allies, in general, cooperated very effectively with there being a significant amount of specialisation from each in a lot of equipment. AFIK the Americans produced virtually all of the Allies' landing craft, which would leave the British unable to actually perform an effective landing.
If the British were to concentrate all of their resources against for a Normandy landing and have American support for the landing then it becomes plausible. Certainly if the formations that in Italy were diverted to Britain for the landing (leaving the Americans to deal with Italy) there would be enough trained and equipped soldiers available for the initial landings. The follow up forces were mostly American and the British would have struggled to have supplied enough trained manpower for the follow on operations.
So Overlord could have been managed by the British alone, so long as they had active support from the Americans, but the breakout and subsequent operations become less and less likely without the American ground forces' contributions.