The good news: the new external handle and lock are a perfect fit for the hole left by the old handle and lock.
The not-so-good news: the spindle on the new external handle is square which means I can't secure the old internal handle to it (the old spindle was circular and threaded). I can use it to turn the cam but it just slides off when the door is opened.
Also, with the new external handle, there's no way to lock the door from the inside (the old handle had a switch on the back of it which, if the lock hadn't failed, would have locked/unlocked the handle).
Before fitting: the door couldn't be opened from the outside and couldn't be locked or unlocked from either side.
After fitting: the door can be opened from the outside but only once: as soon as you open it, the internal handle falls off.

Also, the door can't be locked or unlocked from the inside.
So I'm in a different, but no better, position. I think I'll have to just stop using the garage door until I can afford to replace the whole thing.