Graduated from my masters, and left the country. That's a pretty good reflection of how I feel about the UK's job market right about now..
I mean, that's not quite the whole story. I've worked abroad for the past 5 years, but me and my wife were planning on coming back for good this year. The pandemic quickly changed that, and we left again in the summer. The job market in the UK was pretty dire before the pandemic, and its looking especially bleak now. Wages are low compared with what you can earn elsewhere, and living costs are really high, so no wonder people are struggling. Sure there are a handful of sectors that still pay pretty well, but for the majority of normal people, its not great, its a lot of work for a very un-inspiring quality of life.
The job market isn't the only reason we left, it was also just the general mess of how this pandemic was handled here, and the fact that there is no clear end in sight for countries like the UK, except for keeping our fingers crossed for a vaccine.
That's my advice for graduates in the UK. We as a people are far more reluctant to move abroad to work than most peoples (aside from Americans, who make us look very international by comparison), but there is a wide world out there with plenty of options. If your struggling in the UK, check your options abroad. You might find that you can get more money elsewhere, or that the type of work you want but can't get in the UK, suddenly becomes an option somewhere else. etc. In difficult times, try not to limit yourself.
Obviously some people can't, with family/relationship reasons, but if you can.. take a look at what is out there. because its going to be a tough tough few years back in the UK.