To put some perspective on it, I am Gen X/Boomer cusp. Bought first flat (one bed in very run down rough area, over a shop) aged 29. Had first child at 39.
In my twenties, to get out of debt and into credit I spent a year working three jobs - one day job, one evening job, one weekend job. I barely saw friends, spent nothing on myself, but it was with a very strong intention, with a self-imposed deadline, and it worked. Short term discomfort in order to turn my life around. I felt like a superhero by the end of that year.
Could you cut back on everything, sell things you don't need, eat as cheaply as possible, take on extra work evenings and weekends, but see it all in a really positive light, as your deposit grows. Do it only for six months or a year, and keep a small amount - say £15 - for a little treat each week. I was told to do that and it really helped - just a pizza at a food market with a friend, or a swim or a bunch of flowers or bottle of wine.
Try not to think of your current situation as impossible, that your time is running out or that everyone before you had it so easy. That isn't the case and it doesn't help you feel motivated. Your eggs will be fine for a good 12-15 years.
My first owned home was in an unfashionable run down area that was close to nicer areas and was not actually dangerous. When I met DH he'd done similar. He had a flat on a main road in an area of London that was served only by rail not tube. That's how he afforded it. It was a starting point.