Alex, your current insurers will usually insure it as a temporary additional vehicle for a small fee. Depends on the company but many let you do this from 1 to 30 days at a time. I used to have Direct Line, when I was trading to my clio from my old car, there was a 2 day delay and they reinsured my C2 as a TAV for 2 days for £5.25.
Do not get someone to use their own "driving other cars" cover, it needs to be insured seperately by the owner (now you, not the last owner) for this to be valid (though there are some dubious tales to the contrary for some companies floating about.)