Not so much a case of Ovals dying out, more that it never really caught on as well as it did in the states.

There was never a huge amount of oval racing in Europe, Brooklands and Monza are probably the most famous. Monza, whilst having an oval configuration always had a road course as well, Brooklands was an oval of sorts, albeit with a kink in the straight before the pits, but it also had infield configurations.

Most of the circuits in England are a result of the war - disused airfields after the war started to see races being held on the perimeter roads - Silverstone, Thruxton, Mallory Park, Snetterton, Castle Combe and Goodwood were all airfields, as was Santa Pod (the UKs best drag strip and one of the best in Europe). Donington Park and Brands Hatch were used for training and/or vehicle storage during the war. Across Europe the same thing is repeated to some extent, other circuits (both in Europe and the UK) were borne from public road races - indeed, parts of the Spa circuit were still public roads up until the early 90s where it was made a full time circuit.

I found this thread that may interest you : http://forums.autosport.com/topic/169646-oval-racing-in-europe/ It discusses ovals in Europe, the interpretation is somewhat vague though, given the layout of the mentioned locations, they also spend some time talking about private test tracks (used by manufacturers to test cars) rather than racing circuits.

Also note that in England we do have somewhat of a dirt oval scene - its taken on the name "hotrod racing" but its closer to late model dirt track in the USA, there is also sprint & midget car racing. This is very much a niche/clubman sport, you'll never see coverage on TV. Motorcycle speedway (again, on dirt ovals) is probably better known and you may see some on TV if you search, but again its not mainstream. There are domestic series of speedway in Poland, Bulgaria and is quite popular up in Sweden/Finland and further away still in New Zealand at Australia.