Private Sale with Private Plates

So I'm looking to buy a car that currently has private plates on it. The seller has said they'll transfer the reg online on the day of sale. Doesn't this mean a new log book will be made with the original reg which I won't receive until they then do the change of ownership that sends then a new log book to me?

Is this a process people do and is it safe. I'm not thrilled of the idea handing money over with technically an invalid log book.

What would you do