When can the NHS get you in? Where in the process are you currently? Has he had his initial biopsy/wide local excision? Are they considering or have done a sentinel lymph node biopsy? This is different to the FNA biopsy you are discussing here. Has he had CT scan and/or brain MRI?
Me personally, I’d be making myself really annoying (in writing) to get the FNA booked in under the NHS.
I have stage 3c melanoma (primary melanoma that spread to a local lymph node). The timescale you mention is completely normal. I’d expect 10-14 days for FNA results. That’s normal. Realistically, the biopsy itself is not hugely helpful. You know he has melanoma. Having another positive biopsy isn’t going make a tremendous difference unless you plan to fund further surgery and treatment privately (hugely expensive).
It may give you answers, but it won’t give you solutions. What you need to know is when he will be seen by plastic surgery, when he will have scans, when he will be booked for further surgery, when he may start treatment (this is usually 4 weeks after surgery to allow for healing).
I had my initial biopsy in mid August (of 2024), results back mid September, appointment with plastic surgeon by end of September, CT/MRI/FNA biopsy, in the next week to 10 days, second appointment with plastic surgery early October, big surgery (wide local excision and lymph nodes removed) was end of October, started treatment end of November. This is a very normal trajectory with no delays. There will be very unwell people also in the queue and they do sometimes need to be prioritised as well.
So sure, you can go for the private FNA, but it isn’t going to make him better. What’s going to make him better is surgery and treatment and you will almost certainly need to pursue these within the NHS.
If you do want to seek care privately, the Royal Marsden is very good and there is another one in Bristol that I can’t remember the name of. What I would really recommend though is making yourself really annoying. Call the consultant’s secretary, call the nurse team, call and email anyone whose numbers and emails you can get with updates. Be polite and gracious but update on every new symptom. Ask when things should be booked, how you’ll be notified of the booking, etc.
If you have melanoma specific questions, I really recommend the group Melanoma Focus, which has a helpline and an email where you can email for info and support. There is also a group on Facebook called Melanomamates, which is run by folks with Melanoma Focus and is great for up to date information. There are people on there who were diagnosed 20 years ago and if you have questions people will chime in with both personal experience and also scientific articles from recent research studies. You can join as both a patient and as a carer (so you could join on his behalf).