It's a sad fact but if you are accepting what they tell you then they will get away with this.
You have to shout loudly and make a fuss. I know this isn't always easy if it's not generally in your nature, but trust me, it will make things happen.
Make a start by phoning your GP's surgery. Tell them a wait of 4 weeks is unacceptable and DEMAND an appointment in a given timescale (2 days for example). If they refuse, stay on the phone, be persistent and as a last resort threaten to go to the surgery and sit there until you are seen.
They will miraculously find a free appointment for you.
Good luck.