It will have been a ‘VAT qualifying’ car on which VAT is paid and
reclaimed until the car goes to a non VAT qualifying owner. This actually makes no difference to you, just the way the car is invoiced. Had you been a garage or a leasing or hiring operation, you too could have claimed the VAT back, then charged and repaid VAT when you sold it. The dealer got it on a bulk registration fleet deal, the terms of which were that it was registered to a 'fleet' for four months. That's how he obtained the discount that he passed on to you.