I think there would be a lot of different outcomes from different people all doing what they think is best and only some of them following the rules. Sometimes the rules may not be very close to hand or obvious either.
Experience says that when going into Biggin from the north we always get vectored towards LAM to leave on a heading (normally 180 or so). There are special lost comms procedures for Biggin however, which would probably create much more workload for us doing something different and probably be unusual for ATC too. I know a lot of people would lose the radio (assuming already in London airspace at the time) and just go direct LAM as usual to leave on 180 and do the ILS.
New rules would probably be good but it's one of those things which a blanket rule won't really work IMO.