What's my legal position

Hi, I'm having a bit of a tussle with Volkswagen Financial Services (VWFS) over an invoice they have sent me. I had a lease car from them, and at the end of the term it was inspected and there were some minor signs of wear and tear that needed fixing up as agreed in my contract. I disputed some of the damage and we reached an agreement which was confirmed via an email to me: Thank you for your email and photos regarding the end of contract vehicle WXXXXXX Audi A3, I apologise for not being able to get back to you sooner. BCA Inspection report came in at £941.00 + vat in refurbishment charges; I can confirm that your enquiry has received a thorough review in accordance with our procedures, and that BCA send in only qualified inspectors for the end of contract inspection, however we would like to resolve the issues and as a valued customer, I would like to offer you a credit of £589.00 + vat if all outstanding charges of £312.00 are received within 10 working days of this mail. Breakdown 2 tyres £302.00 + vat 2 alloys £120.00 + vat Wing Front n\s £35.00 + vat Door rear o\s panel £265.00 offer 50% 132.50 + vat Total £589.00 + vat credit This offer excludes any outstanding rentals or contract early termination fees,these are non-negotiable and must be paid separately. I hope this offer meets your approval and draw this issue to conclusion. I then paid all outstanding charges of £312 using my Mastercard the day after receiving this email over the telephone. The chap on the other end of the telephone agreed that all I had to pay was £312 and took this off my card. I noted the date and payment reference Auth Code. I have subsequently received a letter from a solicitors pre-legal team asking me to pay £374.40 i.e. £312 + vat. At the time, Volkswagen Financial Services offered me a credit for the VAT which is why I believe I only needed to pay £312, however the solicitors are now claiming that I still owe £62.40 to cover the VAT (After I gave them the payment reference). My question is, does the above email which states: all outstanding charges of £312.00 and has the words vat credit prove that I do not have to pay the remaining VAT? I can pay the £62.40, it's not the end of the world, but clearly I'd rather not, since my understanding was that this did not have to be paid. Does the fact that VWFS accepted my payment of £312 also confirm that I do not need to pay the additional £62.40 since they did not raise this question at the time of payment? Just wondering what my legal position is on this given the above information. Thanks Chris