I think you are right on the symptoms, and some of the causes, but let me add some from the other side, as I think left and right both make good points and you have to be intellectually honest if you want to move forward.
There are some multinationals who escape taxation, but even if that were perfectly addressed it wouldn't solve the UK's issues. Tax receipts are already close to 40% of GDP, these are record highs, frankly there are few countries where going over 40% is both possible or sustainable. (The US is at 25% for reference).
House prices are high because for 15 years mortgages were basically at 0% interest. This didn't actually make housing more affordable through cheap mortgages, if just inflated house prices. The endless schemes to help young people buy property just makes this worse, as the schemes are just built into the price.
Lastly, and this is usually hard to hear for people of your persuasion, you just can't add 500k-1m NET people to a country and expect housing to be just as available, and the health service to not be under massive strain. It's a physical impossibility. YES, I know many immigrants work in the NHS. That is not a valid rebuke to the problem. 1m net immigrants last year is 1m more people who need health services. The NHS has received massively more funding since covid and just can't cope.
I'm not against migration, but the sheer numbers need to be talked about. You can't keep a sustainable country at these levels.
Finally, the UK has relied on financial and advisory services for decades as the core of its economy. This seems to be working less and less, tech is taking over. the 80-90s were about finance, since then it's been about tech. Slowly the country is falling behind.
This is a chronic issue in almost all of europe, but at least there there is high end manufacturing, and eastern europe has tonnes of catching up to do which grows the economy.