Ken, This is my local supplier in Oz.
www.deebee.com.au You will see the range of corks they supply. I'm sure you can find similar in the UK. You just haven't looked hard enough. You get the cork that is just too big to fit in the hole and then boil them until they are soft,(ten minutes or so). You can then effortlessly squeeze them in place.When they dry out in a day or so they will be immovable. After that trim off the excess with a sharp knife (watch the fingers) then finally sand to thickness. Dead easy.
Do NOT sand to the slot size first and then just pop them in place. That is the path to rapid failure, they need to be over size and squeezed in so they can't move.
Tell us how you get on.
Cheers,