If your training school has an association (eg if you trained at SMAE you can join the BPCA) you will be welcome there. You may also be welcome at the Alliance, and vice-versa.
As an FHP you cannot join the SCP, you may be able to join the Institute.
These are the four main associations in the UK.
I don't have all the addresses to hand but if you use Google you'll find them easily enough.