Does Europe not have VORs?

Of course - though many of them have been decommissioned or are in the process. Though recent developments have probably reduced the enthusiasm for removing them so quickly.

However, that doesn't change the fact that the intersection that ATC are flying you towards are actually now defined as coordinates, not radials or distances from nearby VORs.

If an ATC tells you "direct OKSAW" they won't give you a VOR radial to intercept - you are expected to go straight there in a relatively straight line from your current position. There were boxes like the KNS80 that could do VOR-VOR navigation to do this kind of thing but it's not user friendly by modern standards.

When you file your flight plan, there is a box for "equipment". Put "O" there and they will not do that to you anymore. "DO" if you have DME.

This won't work in the UK/Europe. B-RNAV has been a requirement since 11 April 2011 at all ATS controlled routes and levels (previously only above FL95). The only reasonable equipment is a IFR capable panel mounted GPS.

Of course the UK is extra weird because you can fly IFR in class G airspace which is quite extensive outside of terminal areas. More realistically this is VFR in IMC, with the pilot being responsible for his own terrain and traffic separation (somewhere between relying on the "big sky" theory and these days, hopefully, some TCAS system). We even have a special sub-ICAO IR(R) rating which allows a pilot to punch holes in clouds and even to shoot an approach at a airport but not to access the class A TMAs / airways.

Oof...since 2011? Even with everyone knowing that GPS signals are -125 dBm on a good day and anyone can jam them? Jeez! My condolences. At least here stateside one can still fly IFR with a VOR/DME just fine.