If you're going to be running the 5-speed box, then it will probably die a very brutal death with those projected power figures
If you're eventually looking for about 600bhp (if you are in fact serious about all this), then you will need to have a getrag 6-speed conversion which will cost you a fair whack (used the search bar), or the other option is to go with a built autobox, also not a cheap option. Bearing all this in mind, the best option for you would be to sell your n/a, add that to the £8,000 you have budgeted for the conversion, and buy a tidy TT 6-speed from a member when one arises.
When you add it all up, including your future plans: TT engine transplant, single turbo conversion, 6-speed conversion, TT diff, UK TT brakes etc....etc. It all becomes very expensive, the investment in a decent 6-speed TT now, will probably save you cash in the long haul