The thing is that if every single person in UK struggled a bit more, situation wouldn't change regarding housing. Those at the top of the heap could still pick the best housing (at even more elevated prices as now) and the poor ones would still be ending into the exactly same shack that they live now in. And the rent / price of it would just be exactly as much higher as everybody's income increase from this "extra struggling" allows.
Only if this extra struggling would be specifically concentrated on building more housing, it could make a difference by increasing supply where demand is highest and thereby lowering the prices. But since most of the "struggling" is aimed at completely different things, it doesn't really help with the supply, but just with the ones personal positions in the queue of strugglers looking for housing.
Personally I'd disregard increased earnings on a national level as a solution to housing problems. I'd even go as far propose that price of housing is determined by peoples wealth / capability of paying -> no amount of increase in GDP will help, because it will just increase the housing prices accordingly.
This hypothesis might even lead to a conclusion: Increasing the construction sectors portion of GDP might actually lowers the price of housing, because then we'd have more housing being built / maintained / enhanced / etc. compared to everybody's earnings, which should lower the prices by normal supply / demand interaction.
About plumbers:
How many of these £70 and £500 gigs does a plumber do in a month on average? How much goes to maintaining equipment, car and fuel? How much time goes into writing the actual invoices, ordering the necessary parts or getting them from supplier.
It makes very little sense to compare the invoiced hours with the salary, unless you talk about contracting where you have some kind of fixed number of hours in the contract.