If you post photos of what you currently have, maybe we can get our collective brains together and think of a solution for you... One thought that came to mind was that since the battery was apparently shot to begin with, this may have been the reason for the poor performance of the light.
There are some other threads on this board related to others using a UK body with LEDs. One that comes to mind was written by Rodex99 entitled
cooling tested in uk housing where the bottom line was:
So it'll be a trade-off between the performance desired and the degree in which you want to modify your light, as well as the attendant expenses involved.
That said, I need to add this as well: I'm relatively new here to DIY-ing lights as well. The other posters have been doing this much longer and definitely know what they're talking about. And one common thing they say is that to DIY this light properly will cost you some money. You've stated that you want to try to save your initial investment of 40 quid - an amount I wouldn't pay for an old UK600, when they can be had for 15 quid (but then again I'd have spent the money on something else). Considering you have to replace the battery of the light already anyway, you really need to determine whether or not you wish to continue with this project in order to save money. If it was for the learning and the fun of DIY, then by all means, proceed. Otherwise, get a new light.