Honesty is the best policy! Advise controller that it will take at least two minutes to set up and brief the new clearance. In ATC terms that feels like an hour,especially if you're lined up.
A couple of observations I could make. The original clearance seems like a cop-out from a controller who didn't know what to say an hour before...the clearance seems to be a tactical solution which could not possibly have been identified so early. Second...how often do you see controllers on the flight deck these days? Third...Some modern controllers have very little interest in the job other than the £100k salaries, they might not actually realise the enormity and significance of their actions in a case such as yours.
Solution....Stay cool.....absolute must is to put the details in voyage report or feedback to chief pilot/liaison/OPS or whatever you use. Process locally might work...but a paper trail through to relevant regulatory authority such as UK CAA is always advisable.....your experience can help everybody.
Just a question for you.....an assigned heading is only good for maybe three minutes [in the event of radio-fail] ...what would you have done after that? I guess an option would have been to revert to the most appropriate SID.