I've been in this situation before having moved from Australia to the UK in my early 20's and I have been here 8 years now. I moved here knowing nobody. I didn't have many friends in Australia for the exact same reason you mentioned, but I was never assertive about fixing it. I just thought that the 'fun' part of my life was over. In the UK, I have managed to make more friends than I ever had at home.

I found that if I ever had colleagues that I got on with I would be a bit assertive in organising drinks/pub quiz after work, and be sure to invite everyone. The people up for a laugh are keen, which filters out anyone who is boring. I imagine this can be applied this to any situation where you see people often enough (sports club etc). I've found there is nothing wrong with being honest and at some point mentioning the situation you're in during the conversation, not in a pleading for friendship way, but as you've said it is a very common experience so it is surprising that others might be in the same situation but are scared of taking initiative, or they might just be empathetic to your situation. It was always easy to say for me though because I'm not from the UK.

It might be luck, but when I've bought this up it seemed to spur effort to build the friendship (and this is colleagues between 25-35 both single and in relationships). That being said, I once moved to the Netherlands and this didn't work at all and it was because everyone was from the city I lived in so they were not remotely interested in making new friends and didn't have any appreciation of my situation. This is the same as Australia because nobody ever leaves where they are from. Now I think of it, all my close friends in the UK are British and European, but they have also moved to new places and have experienced the same situation. I guess we would all be alone if we didn't take initiative. Even when my friends have moved from where I live to new cities, the UK is so small that everyone is really only 2 hours away at most so I've always thought there is no excuse. I've gotten flights to Germany before I catch up with friends.

My advice would to align yourself in a situation where you might meet people who are similar to you, be a bit assertive (it's painful) and the sort of people who are going to be interested in building a friendship and have some empathy are the sort of people who make good mates! And the quickest way to build new friendships is to just be interested in others and ask questions.