I sympathise with you OP. My parents have had good experience with the NHS in the past, but I know that other people's experience can fall woefully short of that.
This is where I can appreciate the US healthcare system. If you're fortunate to have the funds for self-paid treatment or good insurance coverage, like my family and I do, you can get seen quickly, and with a nationwide PPO plan like ours, self-refer to almost anyone. We have many choices.
Many friends in the UK laugh when we tell them that we have a $3500 annual deductible and insurance won't pay for anything until we hit that amount, but given the variable, but generally greatly declining state of the NHS, I'd rather that because we can see specialists in days or weeks, and not have to wait months or even years.