I'm afraid this is going to confuse you even more.If you have 12v transformed existing light fittings, the ones you linked to will work with the same tranformer and bulbs.
In terms of the bulbs I'm afraid that is not the case. The lights that the OP linked to here:
http://www.tlc-direct.co.uk/Products/FRSH01W.html
Require halogen aluminium reflector bulbs
Where as the bulbs the OP says he has currently are these:
http://www.tlc-direct.co.uk/Product...rds&kw=l58dl&gclid=CI-085nn0q4CFeMmtAodZXJ5_g
Which are dichroic lamps - and are NOT suitable for that light fitting.
Also while there is a high probability that the transformer is suitable for the new lights they will need to be checked before fitting.
To the OP do you ever get the feeling that it might be easier just to leave the lamp as it is or as Chris5 has said use heat proof paint and respray the light unit facia.
Or alternatively get an electrician in to sort it out for your?