Car & Classics is probably the number 1 site in the UK, but eBay is pretty good too, though you need to spend time sorting the 'proper' classics from the wannabe cars that are really only fit for banger racing. Consider too Classic Cars for Sale which is probably the second most popular UK site.
And don't overlook the auction houses. Although they frequently advertise *some* of their stock on Car & Classic, they don't generally advertise every item they are handling. The major ones are Brightwells and Bonhams, and there are loads of other smaller ones. Look here for a better list:
https://www.classiccarsforsale.co.uk/auctions.
Then there are local dealers - near to me in Sussex there are Nutley Prestige and Sussex Classics, but most areas have one or two dealers within a reasonable distance, and these dealers often will advertise only on their own web sites.
Lastly, don't forget Gumtree. Generally cars on here are right at the bottom end of the market, but don't forget many people would not regard the 126 as a classic but merely a rusty old heap they want rid of for fifty quid. It doesn't happen often, but you *can* find some real gems on Gumtree from sellers who don't appreciate what they have in quite the same way that you or I might do
