Is the garage (Evans Halshaw) you bought the car from a Seat dealer? If so, then presumably the car was sold as a Seat approved used car and went through a multi point inspection (when the service history should have been checked by the dealer) and was sold with a warranty - I think the current warranty is 24 months for used Seats sold under the Seat Approved Used programme. If the car didn’t pass the multi point inspection then the dealer shouldn’t have sold it as an approved used vehicle.
If the branch of Evans Halshaw you bought the car from isn’t a Seat dealer, then presumably it was sold with some form of (12 month?) warranty rather than just the balance of the original three year Seat new car warranty (car serviced 6 months late in July which would mean it was first registered in Jan 2019 so there’d be around 4 months of the original warranty left). I’d expect Evans Halshaw to provide a 12 month warranty on ‘nearly new’ used cars they sell.
Either way, it’d be worth checking the small print in the warranty documents for your car to see what the position is regarding late servicing in relation to warranty claims. If a late service means a warranty claim would be repudiated by the warranty provider, then in your position I’d be speaking to the dealer and asking why they sold a car with a warranty you may not be able to rely on in the event of an issue. If this is what’s happened then hopefully Evans Halshaw will do the decent thing and honour any warranty claims for the duration of the used car warranty supplied with the car when you bought it. I’d be asking for confirmation this in writing.