1. Use "Question for Seller", on the item description page, to ask if the Seller would kindly consent to letting you bid on his auction well before auction end.

2. Point out to them that you know it is not on offer to UK buyers, but that you are seriously interested in it.

3. It is best if you can pay using a payment method the seller accepts. (You do not want to add extra reasons for the seller turning you down).

4. If applicable, a promise to make a quick payment by PayPal as soon as the Seller has given the total cost will help immensely due to the quickness at which the seller is paid by this method.

5. You should also point out that you will pay the increased shipping costs.

6. Closing line should be that if they will not allow you to bid then apologise for troubling them.

If you do not ask and then bid you leave yourself wide open for Negative Feedback and being reported to eBay under this Rule.
Unwelcome Bidding - Bidding in violation of the terms set forth by the seller in the listing description. Examples: Seller states they post to "home country" only and the bidder is outside the stated postage area. Bidders should contact the seller first and enquire about exceptional postage circumstances

One option is to use a reshipping service like MyUS which is a US International Reshipper, who give you a US mailing address and forward the package on to you.
Alternatively, again in the US, FedEx will collect parcels directly from the seller.

But in the end no matter how hard you try, it is the sellers auction and they are under no obligation to change any of their terms and conditions including the countries they will / won't ship to.