While I was waiting for my appeal I had to tax my PCP car, it was before the recent tax increase so only cost £30pa. When I won my appeal I took the V5 to the post office and they sorted it out, I didn’t get a refund, but as it was such a small amount I wasn’t worried.
New car road tax is a fair bit now but as you can pay by direct debit you should only be out one month’s payment at the worst, as the disabled V5 only takes a couple of weeks to come through.