I've only used an online pharmacy a couple of times, so I don't really feel justified in making a recommendation, but if you Google " online UK pharmacy" you should have some success. Some recognisable high street names offer an online service, so they should be trustworthy.
May I ask what you mean when you say your mother's medication is " nearly over"? I'm just a little concerned that she may have finished a course of medication which you feel has helped, and that you want to continue getting it of your own accord.
If that is the case, I hope you will get appropriate advice before going ahead, just in case there are medical reasons why she should not continue. Having said that, I think many of us here would understand feelings of frustration with the Healthcare System, and the desire to take our care into your own hands,