Location affects the price significantly though - whether you want to call them "luxury" or not, if you build in a desirable area then lots of people will compete to purchase those, a developer isn't going to want to sell at some huge discount.
You could try to force a discount for some limited supply of them - some sort of social housing allocation with some criteria for who can buy - lived in the areas for X years as a local council taxpayer or works as a key worker + some max income requirements - maybe then you have some select group of people earning say between 40-60k or some couple with smaller individual but larger joint incomes who can buy a property etc... you've still got an intractable problem with desirable area and supply - even if your allocation isn't purely on price you might have some huge demand for such properties and have them snapped up as soon as put on sale or you might need a lottery system or you might have just restricted your allocation to such a small subset of people that they sell steadily over time but aren't really available to all the others who would love to live there but aren't eligible.
Either way a desirable area in a place like London is going to be oversubscribed whether you allocate properties by price or you thrown in some criteria to filter people and allocate to some subset you're still going to have people who lose out.
In all seriousness, I hope what you said is true. The UK would be a much lovelier place if every small town high street was full of independent coffee shops, restaurants and shops to keep home-workers (or rather, just 'workers'?) entertained without the need to shlep 1hr on a train into London/Birmingham/Manchester/any other city.