I'm not saying that the Romans bred like rabbits, but I have trouble accepting that the Romans had little impact on our DNA 
The Romans were a well organised military presence in Britain, not a colonizing one, and were out numbered by the Britons. At the end of a tour of duty soldiers posted here were free to return to their families/home elsewhere in the Roman empire. Once the Romans had their big credit crunch they packed up their bags and left to defend Rome, unlike, the Saxons, Normans, etc., who stayed.
The Romans were always deeply unpopular with indigenous Britons. Once their army left, I wouldn't have like to have been a civilian Roman left in Britain, as the Britons took to destroying Roman buildings, collaborators, etc., with great relish.
In addition, most dalliances Roman soldiers had with the locals would have resulted in children born into poverty, with relatively poor prospects of survival.