Kolibear,
there are some interesting comments on that other thread. Some of them quite correct.
First of all, in response to your original post, FIR are a non-radar service. It consists of a controller sat with a headset on and flight strips. Radar is available nearby but not instantly.
D&D have DF, Radar, Comms, telephone lines and low level maps. In such a situation, they would be able to identify you. At the moment the nearest radar is however, in Essex, which will not give very good coverage in the area you mention. Once the radar in Surrey/Sussex is back that should improve matters. DF should give a reasonable position.
If you are working a unit with Radar, it would be better for you to stay with them. They will be aware of your position, type intentions etc and would inform D&D of your situation. You would then stay with that Radar Unit who would be provided with support/direction from D&D.
The situation you mention is a little different and in that situation I might like to get my position fixed as soon as possible. A short Mayday changing to 121.5 may well be in order. It is really up to you as the captain of your aircraft.