I couldn't find an existing thread on the topic of outdoor covers for the 2 Series, so I've started one here. Inviting anyone who has one to contribute and give feedback as there's a huge array of products out there and it's hard to evaluate what's on offer.
In the end I went for a cover specifically designed for the 2 Series Convertible from Car Covers Factory UK, comprising 7 fabric layers including an internal fleece, claiming to be resistant to rain, snow and UV and to a more limited extent, hail. £229 incl. delivery. See here. There are cheaper versions with fewer layers, but it seemed to me they were more suited to a car that's still under a carport or similar. Loking 'round at other suppliers, I got a bit frustrated that a lot of the cheaper ones turn out to be mainly for garage use or were a bit vague about how well they'd handle bad weather.
The 2 Series has a rigid aerial that can't be removed, so you have to cut a hole in the fabric, and then apply a special patch supplied with the cover. As well as a strap under the body of the car, the kit came with a security wire to thread through the grommets in the base, with a lock, if you're worried about theft/vandalism.
After a few weeks, it seems to be holding up well and has been stable in some pretty heavy weather. The elastic tie around the base is pretty good and the fit is tight enough to be secure, but lose enough to allow a bit of ventilation. Of course, the real test will come this winter .....
I'm trying to run this car to 100,000 miles, so while the cover is quite pricey, averaging it out over the remaining 60K miles makes the cost look a bit more reasonable. As long as it lasts, of course.