In reply to JimR:
I bought an old Raleigh Dyna-Tec for £70 off Facebook. It's a steel tubing bike with a low front end, single 54t chainring and an old 8 speed cassette. It took over a minute and a half of my PB (which was on a modern, fancy all carbon roadbike).
I think there are a lot of myths out there about how to spend money when it comes to TT racing. Wheels are nice, but in terms of the seconds gained to pounds spent ratio they are one of the least effective ways of "buying seconds".
For the most cost effective ways to go quicker, its hard to find anything as good as:
Lycra shoe covers! They only cost a tenner from decathlon and are worth several seconds. If you love spending money you could by a few more seconds for lots more pounds by getting some of the rubberised ones that go up to mid calf.
A good fitting aero helmet is worth a lot too. Second hand ones are picked up very cheaply.
Getting your skinsuit modified to made sure it's really tight. Pay a professional seamstress less than 10% of the cost of your wheels and shave twice as many seconds off your PB.
Speaking of shaving. I hope you've shaved your legs - seriously, wind tunnel tests have revealed that they can take nearly 30secs of a 10 mile TT in certain conditions.
When you've done all that, I'd suggest buying a dedicated bike, but I'd go for something very cheap to start with. Ideally steal with a low front end and put some clip on aero bars on it. Play around with the position a lot. Watch your PB tumble!
Old bikes are still damn fast if you ride them the right way - look up Alf Engers for some inspiration! Not a carbon weave in sight!