Oh no! You do have my sympathy.
I am in a similar boat to you with unpredictable and sometimes very heavy bleeding. I've tried the mirena coil with zero success for a year now. After a huge, long and unstoppable flood a few days ago (I almost called 111, seriously) it is being removed in the next few days and I will be pushing as hard as I can to get back to seeing a gynaecologist.
I'll go private if I have to. Not that I can afford to pay for it myself, but we have private medical insurance via DH's employer (an American insurance broker) so might as well use it if needed.
I'm in the UK too. Essex. The situation is shit. I've been told that it could take 6 months to be seen on the NHS. If that happens I will definitely explore the private sector.
Maybe take your Dad up on his offer if it isn't money he would miss. Offer him a repayment plan if you would feel more comfortable doing that.
I assume your GP is aware of how much bleeding you are having. Can they help to get you seen more urgently? You've probably tried that though.
How bloody awful and frustrating that they cancelled your appointment at such a late stage. I suppose all of it down to a chronically underfunded NHS which was last year repurposed to be the National Covid Service and has virtually shut down far too much else.
That seems to be the case no matter whereabouts you are in the UK.