As above even if you did only have teaching 2 days a week in one term, it would a) probably not be the correct 2 days and b) would likely change the next term. Even for part-time studies at most unis you can't guarantee which days you would be taught on, even for a single term.
Birkbeck is your best option, since they only teach in the evenings which gives you much more flexibility in working during the day (you could even in theory work full time, although on top of the degree studies that'd be a big commitment!). The OU might also be worth considering since that is self directed and you can decide when you want to do your studies during the week around your other commitments (there are scheduled tutorials now and then but they always offer a range of times and days including evenings, weekends etc).