I can tell whether they've modulated to the subdominant, dominant, relative mahjor/ minor/ supertonic minor etc. But i can't name the new keys. Please can you help me with some tips on how to quickly name the new keys? - inparticular the supertonic minor/major

If you know the key the piece starts in, the supertonic is one step up. Major or minor, your ear will tell you.

The examiner will tell you the key that he/she will play e.g. Cmajor, it's relative minor would be A minor likewise for D major it's relative minor would be B minor (go down 3 semitones from the major key).
Subdominant key of C major would be F major , dominant would be G major, supertonic would D minor. Understand now?

Are you sure you have to name the new key?
Surely if you've correctly identified that you've modulated to the relative minor (or whatever), that will be enough?

no u definitely need to name the key...that's really helpful thnx...

The syllabus states that you must also name the new key.
If you are playing at that level and not able to name the related keys I think that there is something seriously missing.

I learnt the sign language for the letters A to G and intend to hold my hands in the appropriate position while the examiner is playing. Then if I forget what key it started in (quite likely through nerves) I have my hands to remind me!

Yes... The examiner will tell you the original key before s/he begins. Something like "This is the key chord of F# minor".

After you have identified the modulation, you will be given time to think about what is the new key... There is no short-cut that I know of, but you may count your fingers (of whisper) while you are thinking - such that the examiner will know "you are thinking". In fact you don't have to hurry too much on that.

How I did it, was took the key note as one and counted up. So supertonic is the second note of the scale (in C major, D major) , dominant is the fifth (G major)

So long as you know you scales (and what number the degrees of the scales fall on) there is no problem.

hope that helps, though I know I haven't explained it well.

Thanks for clarifying the point about naming the new key. I have NOT been doing this with my piano teacher...but I will do so from now on!