If you've already given a payment source when you try to make the offer, yet eBay is still playing Silly Buggers and is refusing to let you submit your Best Offer to the seller, then there may be another way to get around the problem.
If you haven't already tried it by the time you read this response, put the item in question on your Watch List if it isn't on it already, then log off of eBay UK and log in again via one of eBay's other websites. Whenever I've had to use this workaround in the past I've always logged in via www.ebay.com, which is the USA version of the site. The only difference is that the price will appear in US Dollars as opposed to Pounds Sterling, but if you use a currency converter to work out how many US Dollars you need to submit as your Best Offer to make up the equivalent of what you want to offer in Pounds Sterling for the item, then if the problem is due to a site glitch specifically affecting eBay UK you may well be able to get around the problem by using another site that has not been afflicted by the same glitch that is causing you problems with being able to successfully submit offers on items that you are intererested in.
One other point to remember, though, is that once you have confirmed a payment source when you make an offer, eBay will remember it forever and will take your money from it automatically if you make any subsequent Best Offers on any other items in the future and the seller accepts the offer. Therefore, if you would rather eBay did not keep on doing this, then if you use a credit or debit card as the payment method delete the card from your account once the payment has successfully gone through. This will then break the link between the card and eBay, in which case they will not be able to use that card again for automatic payments. You can, however, just add the card back onto your account again once the link has been broken if you still want to use it; however, if you do so then be careful that you don't use it again for the purposes of making a Best Offer, otherwise you'll have to repeat the process all over again.
In the event that you select PayPal as your payment source when submitting a Best Offer then should the seller accept the offer eBay will automatically remember PayPal as your funding source. In that case log into your PayPal account and go to Account Settings. From there go to Payments and then to Automatic Payments. Find eBay's name on that list, click on Cancel and it will then stop automatic payments from going through to eBay. You would still be able to use PayPal to pay for items being sold on eBay after doing this, though, although you would just need to go through Checkout in the normal manner and select the PayPal option manually in order to give PayPal the green light to make a payment to eBay.
