There's loads of houses being built in the UK (often of questionable quality, built for maximum profit, packed into minimal amounts of space). It may still not be enough to match the demand, but the real problem is we don't seem to be building any infrastructure to support these homes. More people and more homes requires more roads, railways, hospitals, police stations, power stations, sewer capacity, even reservoirs…
Infrastructure isn't perfect, but we talk about housing shortages because people earning double the national average wage rent rooms with other professionals in houses designed for a single family whilst trying to save up double their annual wage for a deposit on a >25 year mortgage on a flat. Whereas for all the UK's infrastructure problems, power brownouts due to lack of generation capability or lack of a local pol…
If you think the UK transport network is OK, but pick the most extreme examples of housing costs, you're probably a Londoner. The housing situation is awful elsewhere, but still a long way from London's extremes.
But if you live elsewhere, try getting anywhere by road or by rail, and it's usually a grim experience.