The main reason for inflation in this case is simple, there is not enough housing, food or oil about, we have basically stretched the earths resources to the limit, and so now we, both as a race and as a nation, are going to have to learn to use less because everyone needs the same resources which is increasing prices and so we can afford less.
This country cannot afford to continue to import loads of oil at ever increasing prices in order to make loads of drinks bottles and allow people to make 100 mile commutes.
We cannot afford to build loads more houses on land suitable for farming, and we cannot afford to import more and more food, depriving poorer countries of it.
If we do not learn to live within our means who knows what will happen.
House prices have gone crazy (best in mind what I said about being within the top 50% of household incomes) for us to move from a 3 bed to a 4 bed would require us to borrow again what we borrowed 12 years ago to buy our house. Which is just not affordable for us, and I doubt it is for anyone else.
The increase in house prices isn't entirely to do with population growth, a lot is down to people owning more than one (second home, but also rental properties and overseas investers).
To illustrate how this is the case, we can look at government policy. There's a target to build 300,000 homes a year, now based on the average house occupation rate that could allow population growth of 720,000 per year.
Now much has been made of the government not reaching this target for some time. The last year there's data has the figure at 240,000 (575,000 population increase).
However the last year there's data for had the population increase as 284,000, so if anything the pressure on housing should be reducing (even if it had been increasing prior to that).
Now some are accidental landlords, for example an elderly relative needs care, their home is rented to contribute towards their costs. They then die, leaving their offspring with a property which provides them with an income or that they can sell.
If there's lots of offspring, then it's easier to sell (and the monthly income may not look that attractive). If you assume £900/month of income then between 2 children it's £450/month, however between 5 it's £180/month. Now whilst the ratio to lump sum is the same, unless you've got a need for that lump sum the impact of a £5,400 pay rise over (say) a lump sum of £150,000 is going to be more tempting than one of £2,160 over a lump sum of £60,000. Especially if there's a risk of a sibling being difficult or wanting to be brought out of their share which then requires the remaining siblings to either put up the cash or take on a loan to do so.