An A/C reporting loss of RVSM status in UK airspace would almost certainly be permitted to continue. You may find that you are asked to change levels by 1000' once or twice to fit in with the traffic or vectored to avoid it. However, if the adjacent unit refuses permission, it becomes our responsibility to drop you out of RVSM airspace before the boundary. That may be more easily achieved earlier rather than later.
In the event of an A/C climbing to RVSM levels becoming non-RVSM, you would probably be stopped off at FL270 or FL280 and your estimate passed at that level. Once the next agency has your details we can start to negotiate, but you will probably find that you will get no further climb until you have been transferred to the adjacent centre.