My first salary as SWE in UK at a bank had a >50K base (60K total comp), second job in finance was 120K base (135K total), and now Google is >180K total comp. All in GBP.
It certainly is possible, but getting into that third modal is probably the hardest bit and will likely involve some leetcode grind and loads of rejected interviews. After your first role, it's relatively smooth smailing (but will still involve leetcode grind every single time).
Hard - I don't know which city you're in but £32k is low for a senior role anywhere in the UK. In London that's a low salary for a graduate role.
I'm similarly disheartened when I read people mentioning that £90-120k salaries are fairly common in London (those numbers seem completely our of reach to me) or when I read about salaries in the US.
In London, a smallish 2-bed apartment would rent for £2500/month. So around £32000/year just for somewhere to live. Overall, 2 people living in an apartment within cycling commute of work would spend around £60000/year - not being frugal but not exactly living in luxury either.
There are over 6500 properties with at least two bedrooms listed for rent on Zoopla for less than £1500per month.
https://www.zoopla.co.uk/to-rent/property/london/?beds_min=2...
If you don’t have kids, get one of the several thousand one bedroom places listed for less than 1k per month.
I worked in agencies for most of my career. They're more rewarding to work for, and offer great experiences, but if you want money you have to move into the corporate/startup world.