Nath's method worked, cheers for that. Before I searched on here, I thought that removing the mirror from the bracket might
help - big mistake. In case you've done this, here's how I managed to reassemble the ball joint. Not very elegant, but it worked after many failed attempts with other methods: I tried assembling the joint then fitting the spring clip after, but no joy.
1. Carefully prize out the bezel surround and remove this and the mirror glass.
2. Support the mirror on two blocks of wood or whatever so that the switch on the bottom is in the gap.
3. WD40 the inner surface of the spring clip, then place the spring clip in a horizontal position on the top of the plastic rose that surrounds the socket (looks like a Hozelock fitting).
4. Using a bit of wood to apply force over the whole of the spring clip, strike the wood with a rubber mallet to force the spring clip onto the plastic rose. If it doesn't want to go, open up the clip a bit with a smallish flathead screwdriver (with the blade horizontal), which you can leave dangling in place while you whack it. Tap again as needed to seat the spring fully.
5. Put a bit of WD40 on the metal ball, place the plastic panel* over the shaft, then position the ball on the plastic rose at the mouth of the socket with the shaft in a vertical position.
6. Strike the fitting (with the coiled spring in) at the top of the shaft with enough force and follow through to force the ball fully into the socket. I used a wooden drift with a cutaway to sit either side of the spring assembly - possibly unnecessary, but I didn't want to risk dislodging the spring.
7. Refit the mirror to the roof (see Nath's post, above), then refit the bezel and mirror glass.
*The plastic panel is the bit that clips into the roof panel and covers the hole. First time I reassembled the ball & socket I forgot this component, second time I put it on upside down and nearly broke it. Get this right and do it just once!
Final thought: when the mirror first came off, there was a tiny tensioning spring near the main spring, with what looke like the fitting position for another at the other end. No idea what this/these were for, and they had vanished by the time I finally got it reassembled, so who knows?