Not quite for everyone - if you already had a first degree you had to pay your own fees if you did a second first degree. My wife did a law degree as a second first degree and we had to pay her fees - what was interesting was that the fees varied a lot from university to university. What was really odd was that the best universities were also the cheapest (by a factor of about 10 - from about £400 to £4000 a year).
Also, if you are Scottish and attending a Scottish university tuition fees are still paid by the taxpayer as they did in the old days. (NB I am a Scot and I've never understood how this can be justified).
What I mean is that I find it difficult to justify that kids in Scotland get their fees paid and those in England (and probably elsewhere in the UK) do not.