OK! So I just got back from visiting the garage and thought I'd give an update.
I decided to get the used 'box checked and it's a good job I did! 5th gear rusted to the shaft (or something like that). It had been left outside and had got wet and water had got inside and rusted it. My hope is now that a good 'box can be built out of the used one and the one that was in the car. The one that is in the car now works fine, it just whines really badly.
In other news, the engine is mostly ready to come out:

Do I need new engine mounts?

I do have new braided oil pipes (I think)!
Propshaft bearing knackered... The bearing itself is ok, but the rubber bit is broken:

Crustiness around the front valance:

A few minor oil leaks on the engine (not going to worry about them for now):

All in all, great progress for a day's work!
I am very relieved that I got the 'box checked out. It would have been a huge issue if we'd just plonked it in and found that it was faulty and had to do it all again!
I'm very excited that work has started on the car. Further updates to follow in a day or two.
Andrew