I managed to save 20% of my salary last year through a few methods - mainly segregating my spending into 60% on what you need (mortgage, bills, food, etc, 20% on what you want (clothes/drinks/hobbies/trips), and 20% straight to savings.
I can't praise it enough - I didn't realise how much anxiety I had around money before I segregated my income like that. I'd worry about every treat, or get myself a treat to stop worrying, and lived in this cycle of constant fear about spending. Now I don't, because if I get a coffee or go out for drinks, it's within my allocated budget. I know I can afford it. It also made me value my purchases more, not only because I bought less but because it came out of a set allowance.
I know that for many in cities like London you're going to face a different split, but I think the principle is still fantastic - some do 50-30-20, I did 60-20-20, but just that segregation is really worth a try!