I just wanted to say that you are not alone. I can totally understand your predicament. I don't know about Glasgow but where I am people come and go a lot and as painful as it is, most people who are long-term in a city already have their circle of friends. It's very hard to break into an established set. Having a few sort-of friends, meeting up maybe once a month or two, and it's nice and enjoyable, but it's not enough and and it's too ... polite. Most people seem to be in couples. People generally don't do what you suggest, so you either have to do what they want or be forever alone. It's a tough gig.

I think the best bet is to forget about the past and start small. Find people who are in a similar position (perhaps other Glasgow transplants) into doing single activities with just you. Like playing a one-on-one sport (as /u/RecursiveSnitch452 suggests), or swapping and discussing books, or playing a musical instrument, or going to art galleries. The internet is pretty great (with plenty of caution) for finding people who are looking for similar things. Reddit DMs (to the others here) or craiglist (or even okcupid) are ok for meeting people platonically, and hey, even if nothing happens, or they are boring, or weird, or annoying, or ghost you, then it gets you out of your comfort zone and you learn something about people. Once you find someone (or more) to meet up with on a regular basis, after a while, you can quite easily start socialising with them outside of the activity that first brought you together.

But essentially all this boils down to whether you chat in public to people you don't know. Do you initiate conversation with people?