I am sorry you are having problems getting a GP referral for counselling. Expecting you to state why you are depressed first is just plain daft. For a start a lot of people who experience clinical depression don't actually have a reason. They just get hit by a biochemical storm. People who do have specific reasons tend to discover these through counselling. If they really understood underlying reasons at the beginning they would be well on the way to sorting things out for themselves without counselling.
Changing GP's is drastic and the issues aren't always simple. My GP is not good on psychiatry but he is fantastic on Asthma and Epilepsy, which I also suffer from. Is yours a single handed GP or are there others in the practice ? If there are you could try seeing one of them, you might have better luck. There are two GP's in my practice and the other one is very good on psychiatry. But she isn't good on Asthma and Epilepsy so I can't really use her all the time. Now I see one of them for Asthma and the other for psychiatry.
There are ways of getting to counselling other than by GP referral but you shouldn't have to resort to them. It is difficult to be assertive with a GP when you are depressed but if you keep pushing you are likely to get your referral eventually. My non psychiatric GP tends to refer me for things to get rid of me, but I get my referral so that's fine by me.