Pity you have opted for the DCT as this looks great value for the ask https://www.autotrader.co.uk/classified/advert/202001216420961?postcode=bb120hr&year-from=2010&sort=relevance&model=Z4&minimum-badge-engine-size=3.0&radius=1500&price-to=13000&make=BMW&advertising-location=at_cars&year-to=2012&onesearchad=Used&onesearchad=Nearly%20New&onesearchad=New&page=1
Your desire for twin turbo , Msport ( so 2010 onwards) , DCT , sub 70k & sub £12k leaves you pretty tight for potential cars .
Maybe not impossible but i can't see you having a multitude to choose from