Infrastructure helps GDP, and that is good. However trying to maximise worker productivity for its own sake is pointless. The world isn't black and white and isn't actually filled with dichotomies.
Well, I'd say it is, because the reason those jobs concentrate in London rather than being distributed more evenly across the country, is because your government pours large amounts of subsidies for infrastructure, companies, and leisure activities on London, mostly to attract companies and rich folks. Those policies create economic inequality and enormously high real estate prices.
The government is spending on infrastructure because people keep pouring in and keep threatening to overwhelm the infrastructure. The insane property [rices come from foreign investment and the banking industry.
Jobs breed jobs. People move to London because of the jobs. Companies come here because the workers are here. So people come here for the jobs. It's self reinforcing.
Despite your apparently shitty living conditions, you're still privileged
your premise seems to be that london is magic so anyone living there is privilidged. That's just insane and completely at odds with a little thing I call "reality".