I would look around for the local storage places, farms etc, that take in, say, caravans - they may be advertising in the small ads, internet etc.
It's about now that caravans, for instance, go into storage, hence the possibility of ads.
However, also ask around your area; many people who put vehicles into storage for the winter will do it through a regular contact.
You could also try your local garages - probably not the main dealers, but any small local bike or car repair place.
How about the Yellow pages; the TV has run articles in the past on storage companies, not garages as such, who will store anything - the capital of Scotland must have some of them!
ps I don't think it is an odd request; maybe there is a business in this for the UK, just as there is in South America.
Many years ago I kept a bike of mine in an old barn for quite some time and it did not even have a cover over it (what's one of them?) - it was covered in chicken s**t though.