If getting through by phone isn't working, could you either e-mail the surgery or post a letter through tonight (marked urgent) explaining why you feel you need an urgent appointment (so mention new lump and relevant family history) and asking them to set one by for you. If there is something in writing it might make them think twice as you then have proof that you have requested to be seen urgently.

Make sure you keep trying to call in the morning as well... Hope you get an appointment soon!

If getting through by phone isn't working, could you either e-mail the surgery or post a letter through tonight (marked urgent) explaining why you feel you need an urgent appointment (so mention new lump and relevant family history) and asking them to set one by for you. If there is something in writing it might make them think twice as you then have proof that you have requested to be seen urgently.

Make sure you keep trying to call in the morning as well... Hope you get an appointment soon!

I had this issue. 

I did an e consult and was advised to book a "routine" appointment! Same as you, when I finally got through all the appointments had gone.

So I resorted to going down to the gp and sitting in the waiting room refusing to move. I now have an appointment on Monday.

I know that isn't a great thing go do but same as you I've found a lump and am scared to death!!