"Britain is a crowded island"

As we know, the key elements of the Home-Owner-Ist Manifesto is to oppose a) property taxes and b) liberalising planning laws. One of their favourite mantras is that Britain is a crowded island, which they miraculously use to support both a) and b).

Let's assume, for sake of argument, that Britain really were a crowded island (and let's assume zero net immigration to simplify matters). It's not of course, it's just that urban and sub-urban areas, where most of us live, appear to be crowded because we have restricted the amount of land we can develop down to one-tenth of the surface area of the UK (for purely political reasons without any economic justification), but hey.

Seeing as taxes have to be raised to pay for public expenditure (however high or low, separate topic), wouldn't the use of the "crowded island" mantra to justify restrictive planning laws actually support the argument in favour of more property taxes (and less taxes on income etc).
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To use an analogy: five students have clubbed together and signed up to rent a house with five bedrooms for £200 a week all-in. When they inspect the property, they realise that two of the bedrooms are big and light and three are small and poky.

Which is the best way for them to decide who gets which room and how to divvy up the rent?

a) They could agree (via some sort of auction process) that the two big rooms are worth £55 a week each, and the three small ones are worth £30. Everybody then gets what they pay for, problem solved.

b) First come first served. As soon as the front door is opened, they all burst in and each occupies the best room he or she can find, but they still split the rent equally five ways.

c) As the students parents are too wealthy for them to qualify for grants but not wealthy enough to pay for their upkeep, all the students do part-time jobs at evenings, weekends and holidays. They could allocate the rooms on a first-come-first-served basis and agree that the £200 will be shared proportionally to the amount that each of them earns each week.

If we take the way the rent is shared as a form of taxation, it strikes me that:

a) is the free-market solution and is akin to Land Value Tax;

b) is more like Home-Owner-Ism ("I was here first and it's moi laarnd" funded by a Poll Tax; and

c) is even worse than b) because it's like income tax, which would reduce everybody's net hourly wages by about half, meaning that there is actually little point in working and/or a huge incentive to lie about how much you've earned.
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So, in the analogy, as in real life, there is common expenditure that has to be shared somehow and a limited amount of living space (with some locations being far more attractive than others). If there was an unlimited amount of space, it would have little or no market value, of course, but that house is like our "crowded island".

I fail to see why the tax system of a country, whereby we share common expenditure according to some formula - should be designed any differently.

Just sayin', is all.