The vehicle will be covered by the Consumer Rights Act 2015, so you can theoretically take action against the supplying dealer. The issue in these situations is usually proving that this was an issue before you purchased the vehicle, but it seems like you have proof with the unstamped service book. There will also be the issue of the wear and tear over the last two years of ownership, which may mean they don't pay you the full sum of what you paid if you successfully reject the car. You have legal rights for up to six years (five years if you bought the car in Scotland) after buying.

If you speak to the dealer and you feel like they're being unhelpful/not taking you seriously, I would advise contacting Citizen's Advice for some free legal advice. In fact, I'd recommend seeking some proper legal advice anyway as you're more likely to encounter issues with the gearbox and other components because of the missed servicing intervals.