I have often routed DTY - BPK and on contact advise of this routeing and request via their overhead.
They always used to be very accommodating and the route would be via the overhead of the runway Thr. subject runway in use.
There have been two occasions when ATCO workload has prevented this and a limited RIS offered to skirt around with a dct route when ATCO able to provide a service.
Last time down that way, I decided to avoid entirely and routed dct Cambridge - CLN and stayed at Fl 5.0 the whole way which was much better than upping & downing throught the TMA.
Guess you got no choice though.
Just as well you are prepared for the round the houses route. Keep a damn good look out though - first time we had to take avoiding action and the last time, a couple of months ago, I saw a PA-28 come out of a thin cloud layer to confront an AN-2 opposite direction..........and luckily he reacted.