Our American cousins fly exactly the same procedures in the London TMA as everyone else - ATC do not have one set of rules for them and one for others.
As for how the pilot flies the approach - well that is another matter but believe me there are enough monitoring devices around that what you are saying is not a common occurence - we would see it on radar, HMUs etc.
Maybe the odd aircraft doe s a dodgy approach, but I'll wager it's not soleley and American problem.