No, counsellor and psychotherapist isn't a reserved profession in the UK, literally anyone can use the title - which is partly why they get paid so poorly compared to Ts in other countries and why training and experience is so patchy. It is strongly advised to register because you have organisational support, professional credibility and a clear ethical framework (and support to understand it). Also many courses and most employers now require you to be registered so while the government hasn't imposed registration the industry is doing it itself.

I do think it's important to know what your Ts qualification is, what their practice experience is like and where they're registered, and also to be prepared to move on if it's not working. Finding a competent T can be difficult but registration helps some of that.