My speedo went at 25,000 miles, and I replaced the right angle drive thingy that connects to the gearbox; it's about 50UKP would you believe?
Anyway, on my Ford gearbox (1.6K) there is absolutely no need to do anything to the gearbox.
Replacing the drive turned out to be one of those '5 minutes jobs' that took ages. I replaced the drive (more on how in a mo) only for it to still not work; it transpired that the old cable end was knackered as well, and it promptly rounded the bit of the right angle drive it fits into. So, check the cable as well. I can't remember the cost but it might be worth replacing the whole lot as it's a fiddly job and a pain to do it twice.
Jack the car up - there's a thread elsewhere about this. If you crawl under the car you will see where the speedo cable screws into the drive which, in turn, screws into the gearbox. It's a bit of a Heath Robinson affair as the bit of drive that the cable screws onto rotates - so you try to do up one rotating part onto another.
The drive has a short bit of cable in it (an inch or so long) and it's all just a matter of fiddling around getting the various bits to slot into place. It makes things much much easier if a friend helps you by telling you if the cable is spinning at the speedo end while you twiddle it and assemble the drive end under the car.
Once done, you can test it by running the car on axle stands - but be careful!
It may sound complicated but it is quite straightforward, just tricky to explain here. When you see the bits involved it all makes sense, and isn't much more than "just a case of screw(ing) it into a hole on the side of the box."
I confess that after it had taken me what seemed like all day to fix it the first time, only for it to go wrong immediately, I took it to Hyperion who charged me a fiver or some such, and I would advocate your doing the same!
Incidentally, I have a Sigma bike speedo but can't read it at night so fitted a new Caterham speedo - which is even more inaccurate than the original, showing about 100 mph when the Sigma shows 85!