Car dealer sold me a service plan but now 3 weeks later says its not applicable

Hi all,
I took my car in for a service about 3 weeks ago as it needed a major service (approx £375 list price). I remember back in 2016 before the previous service, the assistant at one of their sister branches tried to sell me a service plan for £360 which covers 1 minor and 1 major service so effectively you get a minor service free plus save about £15 so very good value, I asked him specifically if it covered my car being an "S" model and he said yes. I decided not to take it up at the time as it only needed a minor which cost about £175 and I was planning to sell the car very shortly after but have now decided to keep it for the foreseeable future.
When I phoned up Audi to book my car in for the latest service in December (2017), I asked to have the service plan for £360, brake fluid change, automatic gear box oil change, 4-Wheel drive oil change, MOT etc which all come to about £780! She said no problem and booked it in for the 14th December.
I collected the car about 3 days after the work was done as I had a busy week at work and couldn't collect it as soon as it was ready. When I went to collect the car the guy ran through all the work that had been done on the invoice with me and said my service plan had been set up successfully and it is clearly down on the invoice as "Segment 2 Service Plan Sold, 1 x major service (carried out 14/12/17), 1 x minor remaining". He took my £780 and said thank you and goodbye. This afternoon I got an unexpected telephone call from the pleasant lady assistant at the Audi dealer informing me that unfortunately they have come to set up the service plan with Audi Finance (who administer the service plan) and her service manager has found out that my model (an S model) is not covered by the plan and therefore even though I have paid for the plan, it is on my invoice and they told me when I collected the car that it had been set up successfully, she said this item on the invoice is now null and void and as a goodwill gesture they wont charge me the £15 difference between the list price of the major service (£375) and the service plan which cost me £360! Thanks!
My understanding is that they have entered into a legally binding contract with me because it is on my invoice and I have paid for it and it is their mistake that they did not know that my model was not covered by the plan before taking my money? Even with the legal aspect aside, surely they should just agree to carry out my next minor service for free as a goodwill gesture for their mistake, especially considering I have just spent £780 for all the service items to be carried out by them. Had I have known the service plan wasn't applicable, I would have visited my local independent dealer who would have used the same quality Audi parts but for a considerably cheaper price. Could anyone advise where I stand legally?
Thanks.