This is an old argument. The solution suggested is good, to drive it on your 3rd party cover on the basis that your forward date the sale by 24hrs. That demands some risk taking by the seller as, technically they are still owners until the next day. So if you get flashed for speeding home with your new toy, or have a bang, it's still going to score against them initially.

When I bought a car earlier this year for my daughter we put down a deposit one weekend and then during the week set up insurance and bought the tax ready to pay up and collect the next weekend. Meant an extra 70 mile round trip and paying for a month tax for last week of the month. Hey, it's only money........in the big scheme of things it was a small price to pay compared to the risk/cost should sod's law have us pulled up or in a bang.