I don't know where in Europe OP is, but in the UK, what you will be offered through the GP is often time limited and of limited use. If I had have gone down this route in my area I would have been offered six sessions with an assigned therapist which would have been wholly inadequate. That's not to say it isn't worth asking, but be prepared not to be offered much, and to potentially have a long waiting time to receive it.
Private fees in the UK are comparatively affordable out of pocket compared with the US (although this obviously depends on personal circumstances) and there are charities and organisations which offer copayment schemes which would be worth researching.
If OP is in the UK, I would personally start with the professional associations. BACP for example have a therapist search tool here Counselling and psychotherapy | BACP It's Good to Talk
If OP is elsewhere in Europe it is important to look into how the system works where you are, and what options are available for you locally.