Insure it so the DVLA register that the vehicle is insured, then tax it online. Yes, you are not displaying a valid tax disc, but you are taxed and as such can explain your situation to the police if you do get pulled over.
All you need is the details from the v5 doc, which, I'm sure the seller will provide.
This doesn't work as the tax disc gets sent to the name on the V5. i.e the old owner.
Just stop being lazy and tax it at the nearest PO. Of course you can drive it with tax but the police will take a dim view. It's not like "I have just bought it" has never been used as an excuse before.
I think that they feel if you can go out of you way to pick up your new car, then you can go to a Post Office as well.
It's not a difficult process