Over the past couple of months I've rebuilt my (basket case) A10. It needed a crank grind, timing bush hone, oversize guide (ally head) and guides honed and seats re-cut. This sounds pretty much what you need. I did the sludge trap myself.
The bottom end machining was about £220 and the head under £200. The assembly is straight forward and the BSA service sheets cover it. The challenges were getting parts, some undersizes are hard to find and the oversize guides were only available as "blanks" that needed turning to fit but the machine shop did all that. I got the "blank" TS bush and had the crank ground to -15 and the bush bored to suit.
So my advice is if you know waht you are doing plan it out and then go to a few (there are only a few) engine machine shops and see who gets what you want and is reasonable. I used Classic and Modern Engines in Bracknell, I'm sure you have places nearer to Gloucester.
Save the ally head valve collets, remarkably hard to get replacements.
The end float shimming is tricky, but there's lots of advice on here and a cheap dial gauge is all you need.
If you can its better to take you time and do all the build yourself and only farm out the machining.