With these suggestions for cars 1 and 2 I end up €44 over budget, based on a €1 = stg£0.90 exchange rate. A small swing in the rate would see me in budget. Interestingly, no BMW's at all as the price points to make the budget would mean more clapped out candidates and don't do a lot to stir me, and I reckon these options better fit the brief.

Car 1 - €3425 with VRT and NOx paid - 2006 MX5 https://www.autotrader.co.uk/classif...=e153ar&page=3

Car 2 - €1619 with VRT and NOx paid - 2003 Mondeo https://www.autotrader.co.uk/classif...=e153ar&page=1

Unicorn - €4750 with VRT and NOx paid - Honda Civic Type R https://www.autotrader.co.uk/classif...=e153ar&page=2

or - €4750 with VRT and NOx paid - MPS engine 256bhp - https://www.autotrader.co.uk/classif...=e153ar&page=4