Do you have a source? That's an extraordinary claim, the sort of thing I'd expect to find in Nigel Farage's bag of lies
I believe it's a little out of date now, as some of the lines have been renationalised due to failures of the private sector.
https://en.wikipedia.org/wiki/Arriva_UK_Trains : subsidiary of DB
https://en.wikipedia.org/wiki/C2c : subsidiary of Trenitalia
https://en.wikipedia.org/wiki/Avanti_West_Coast : part owned by Trenitalia
And so on.
(Don't forget that the real profit ends up with the "train landlords", the ROSCOs: https://www.leasinglife.com/features/who-owns-the-trains-ros... ; all of them are parented in Luxembourg for tax reasons)
It isn't an EU thing, though it has at times been something Farage and his ilk have banged on about as if it is an EU thing, it is the way the Tories setup the privatisation of the railways (running them into the ground first as part of making the case for taking them away from the public purse (which it isn't as there are still significant subsidies involved)).
which they did to implement... EU Directive 91/440 ("First Railway Package")
yes, the UK tended to gold plate EU regs, but the spark was the EU