Look for a job, not a visa
I totally empathise with the anxiety and worries international students go through, and I definitely don’t see staying on in the UK as the only option for graduates.
I also understand that a lot of students go straight after a visa once they graduate, but I personally think finding a job you enjoy and like is way more important than finding a way to stay. To be bound by a place under longterm contract is a huge commitment. It should definitely be a place where you can grow, learn and enjoy yourself.
The company I now work at, Scriberia, wasn’t initially on the list of sponsor companies, and I’m really thankful for them going through the whole process in order to work with me. And, of course, my friends and family who always supported me and helped me the whole way. So my thoughts for others who are in the position I was in, is that even if it’s not a sponsored company, there might be room to negotiate a visa if you show your skills, talent and enthusiasm.
More importantly, staying is great, but trust me, leaving is not as bad as you think if you manage to find the right place for you. The year I went back in Taiwan right after Kingston, I also met a lot of amazing, very talented people in a co-working space, Planett.