Hi there,
Im not 100 % sure, I think you'd need to do a little more research and finding out at DVLA etc.
There's no problem at all in buying a mini van, that as Geeta says is the easy part. Insuring it, registering it is where the issue lies. None of the people you mention are UK residents, so they'll have no address etc. So that'll immediatley rule out this method. Unless there has been some new way of doing this for temporary visitors.
I'd say right now, it would be best for you to register the vehicle at your address. You don't have to be the registered owner of course, however as they're are non uk residents again, I'm not sure if a registered owner can be a non UK resident. In that case, you have the vehicle all completley in your name, you can then tax and MOT it just like it was your own. When the band come over, you can get insurances that are temporary, ring them up and add them to your policy for the duration of their stay - probably a minimum of one months premium. When they leave, you take the names off.
Of course, I think the financials would mean they pay for everything as you are doing them a favour, but that would work, be legal and means they don't have to hire each time.
Do your homework though, compare the costs of renting with getting a reliable and well maintained minivan in the long term and take it from there. It may just be that renting each time does actually work out better!
Cheers, DtM !west London & Slough UK!