You can go through your GP, but they may have a long waiting list unless you're a really urgent case.
If your employer has as an employee assistance programme, try that - I had 4 sessions of that after my father died. I went mostly because my manager said if I wasn't shown to be trying to do something about handling my grief, they'd have no choice but to start disciplinary proceedings, as I was basically turning up at work every day and then not doing anything. I think if it had been going on longer, I'd have looked at changing counsellors, and also, I wasn't really ready to see a counsellor yet, but it did keep work happier.
Since my mother died, I have been seeing a counsellor I found through BACP's find a therapist link. I've been really lucky, and we get on well (I chose her mostly on the grounds of location, and that she covered the areas I wanted to explore - bereavement and personal relationships), and we've expanded into other areas way beyond what I was initially looking at.
You might not find a therapist you click with first time - and that's okay - it's okay to try another one till you find one you can work with. If you're ready to look at counselling, and you get a counsellor you can work well with, it can be really great.