Where I live, I have had a yearly mammogram since I turned 30, my local trust has a Breast Cancer family history clinic so I have been affiliated with that for a few years now. Ask your GP if there is something like that where you are. I was on a waiting list for 3 years to get involved, and the week my letter came inviting me to see the clinic, I found a lump in my breast, the care I received was excellent. I don't konw if your aunt having breast cancer would be a close enough family connection for you to have what they might consider a family history. But thats just my opinion, not necessarily the feelings of the NHS.
I don't think that at 27 they feel you would be at risk unless you had some kind of symptoms right now and aching breasts might not qualify, maybe if you told them you had an unexplained dimple or a change in your breasts, or some kind of nipple discharge they might be able to help you further, but if you really want to have one done in a relevant time scale, I say you pay and get one done privately.
Good luck!!!