There seems to be a misunderstanding on the process.
A rejection request letter lists faults, gives the supplying dealer one chance to fix them (not multiple attempts, or only fixing some), if they don’t 100% fix then when you go in to collect car, don’t have to accept it. Can just offer your debit card to process the refund there and then.
The time wasting excuses are just that, outside the basic consumer protection law. You have no contract with Skoda UK, the dealer has a commercial (business) contract with Skoda. It’s unconnected to your (retail) sales contract with dealer. Any waffle they need approval from Skoda is just a lie, how and when they get reimbursed by Skoda UK is not your concern, their commercial contract covers that.
There is no reason why your rejection should be delayed. If you have a separate contract with finance company you may need to settle that. The dealer might have been an introducer (helped arrange a contract between you and the finance Co), but if so any ongoing connection there is also irrelevant.
If you have financed the car, Phone the finance Co and check what type of deal you have, let them know you are rejecting, they will let you know if you settle direct, or can keep the finance running as a loan unconnected to a specific vehicle, in which case can use it for any car (doesn’t have to be same dealer, or even same car brand). For clarity in certain types of finance the finance Co owns car, not you until it is paid for. If it is one of these they will need to be involved in the rejection to ensure they get reimbursed. If you are unsure of type, just ask finance Co when you phone them (they are regulated, by Finance Regulator, so staff on phone need to be accurate).
If the dealer is still messing about, use direct method, walk in, stick both keys on salesman’s desk, and ask if they would like your debit card to process refund. And yes the card machine on his desk can also do instant refunds (probably will require a refund PIN to be entered by dealer, but should have your money in few seconds). The card machine refund receipt is normally the only paperwork the customer needs. Get your refund, then if dealer wants to take 7 weeks to do his internal paperwork that’s their problem.