Winning bidder now says they made a mistake and wish to cancel their bid

The rule is you bid, you win, you pay

You can open a UPI after 4 days and close 4 full days later. They get a strike, you get your fees back, the ability to leave feedback is blocked

http://res.ebay.co.uk/ws/eBayISAPI.dll?ResolutionCenter

set your requirements to block those with 2 or more strikes

http://offer.ebay.co.uk/ws/eBayISAPI.dll?BuyerBlockPreferences

add to blocked list

http://offer.ebay.co.uk/ws/eBayISAPI.dll?BidderBlockLogin

As you have set your listing as private, I am unable to check the bidders history to see if they make a habit of retractions.  You can check this from their f/b profile

Private listings are generally used for items of an adult and sensitive nature, they can put bidders off, as they can also be used to hide shill bidding

You can not force them to pay but to be sure you get your fees back you need to do a non payers dispute.

Open a non paying bidder dispute after four days and close after another four days. You get your fees back and the buyer gets a strike and cannot leave feedback.

At the side of the item click More actions then click Resolve a problem to open the dispute.

You should always sort out one sale before trying relisting or a second chance offer as you could potentially end up with two buyers and one item.

If they both paid you could end up with a non performing seller strike

Never do a mutual cancellation for a non payer as they could decline it and you would still have the fees to pay and they could leave feedback.

Non payers are time wasters.

Do not be tempted to leave positive feedback with a negative comment. This can be reported and removed and you will get a black mark on your account

Most people have their preferences set to block bidders with two strikes.

http://pages.ebay.co.uk/help/sell/block_bidders.html