No chance you can get it on the NHS, I'd say, maybe at some point several years from now (assuming Tories or Reform don't somehow win the upcoming election, in which case the long term survival of the NHS in any capacity is uncertain).
Ketamine isn't officially recognised as a viable treatment for depression here but it remains a recognised medicine and a private doctor will be able to prescribe it, I believe there might be some private clinics around already although I haven't looked personally.
If you find such a place you may even be able to get the NHS to pay for your treatment via the "right to choose" [your method of treatment] legislation, although if you do this be aware you will likely be a test case, as this right has only been successfully invoked for ADHD prescriptions, so far, so you should expect months of back and forth with your GP and potentially higher-ups in the NHS and you may just run into a wall and find it's just not possible. If you do try to do this and are successful though, please do report back!
Edit- OK so I just did a "let-me-google-that-for-you" for "spravato NHS UK" and this was the first result:
https://www.oxfordhealth.nhs.uk/ips/ketamine-trd/
So it looks like it is available for a cost of £3000 / year, although you do have to actually be assessed for it. The fact it specifically says Spravato is not approved by the NHS, might mean that it's excluded from right-to-choose requests, although that doesn't mean you can't argue that it should be included, it just might be a significantly harder road. The fact that there is an option linked to from an NHS website surely means there are other options too if you go private.
Spravato is largely a marketing scam though, if you do decide to be a trailblazer and go the route of forcing legislative change or whatever I'd suggest maybe at some point just switching your request to unbranded ketamine or esketamine which should be cheaper for all involved parties. The NHS should surely know this too but probably talking about the Spravato brand is a better starting point as it gives you an in without immediately being branded a drug-seeking degenerate by some moralistic busybody asshole.
Good luck to you whatever you try and please do report back if you decide to pursue this, very curious how it might turn out.