Hi,
I completed my medical at LL in May 2002, in fact just had to renew.
The chest x-ray had not arrived at the Heathrow centre by the time of my test, so I would not worry too much about long delays. Also make sure that if the x-ray is being sent from hospital to the doctor to chase it up - a copy was promised via my doctor but never arrived.
I waited for 2.5 hours at my local NHS hospital before they decided to tell me they could not offer me one as it was for 'private' reasons. In the end I went to the Nuffield in Plymouth, and was out in 15 mins. I took my letter from NATS and they billed the medical dept. directly.
Good luck.