In an idle moment, I googled "average disposable income UK regions wages rent", the first relevant result was in This is Money:
The survey compared average city salaries against local rent and other standard monthly outgoings for 30 UK cities, calculating the disposable income of city residents after deducting tax, bills and other necessary general outgoings such as travel and food.
It discovered that the average British person gets to keep £1,083 per month after expenses and tax with the average monthly wage coming in at £2,073, while the average essential outgoings, such as rent, travel and food, total £990...
Despite Londoners' earning the highest wage, they also, unsurprisingly, have the most bills and so feature much lower on the overall list. Their disposable income is £1,095, only £12 above the UK average in the study. Their monthly outgoings of £1,629 are also over £350 more than any other city.
Hull is the city with the lowest outgoings of any city in the UK at just £767 per month. However, residents have a lower monthly wage of £1,816 which means their disposable income is £1,049, below the study’s UK average.
Which is exactly what you'd expect from Von Thünen's law - the lowest wage are sets the baseline. In areas with higher wages, the extra wages go into higher rent (other fixed costs are pretty much the same everywhere). The equilibrium is reached when few people are willing to move because the rent saved is matched by lower wages; or the higher wages are matched by higher rent, which is what we observe in real life.
For sure, there are outliers - the survey mentions Derby with the highest disposable income after rent (£1,456) and Brighton with the lowest (£751). This can't be explained by the basic analysis, but boils down to the fact that Derby is considered boring (no idea if it is, but perceptions matter) and Brighton is considered fun, hip and fashionable, plus has nicer weather and a beach. To paraphrase W C Fields, "people would rather be dead in Brighton that live in Derby" and they are prepared to pay £700 a month for the pleasure.
Here is their chart which is quite striking (blue dots = wages, red does = rent plus other fixed costs):
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So the next time somebody says that rents are high in London because of "lack of supply", refer them to this.
You do not need to adjust for "lack of supply", all you need to know is average wages. You subtract £1,800 (average wages in lowest wage areas), which gives you location rent. Add on about £400 for cost/value of bricks and mortar and that tells you local average rents.
To estimate house prices in an area, you multiply location rent by the inverse of mortgage interest rates (currently about 40) and add on the cost/value of the bricks and mortar.