"Rentals are in high demand. " - yes which is why they are expensive
"Rent capping and secure tenancies would reduce the rental stock even further." - no, the houses aren't going to disappear, someone somewhere is going to find a way to make money out of them but by increasing barriers to entry, or in other words if laws make it such that you can less easily make slightly less money out of them, you reduce the incentive for have-a-go landlords to attempt it which has a knock-on effect on demand for "buy to lets" which has an overall depressive effect on prices (whether for sale or rent). I think that is fine.
"you will just swap BTL landlords for people with the money to own a house outright/with a very small mortgage."
exactly, so the margins and the short term cash flow will be less critical or in other words only those who can afford to take a long/ medium term view will be in this business. ultimately if this were mainly councils and housing associations letting on decent terms and will less of a greedy eye on the short term profit I would think this a very good thing
"Round where we live in London, house prices are high because of foreign money" - it is iniquitous that working people's potential homes are artificially expensive because london is being used as a play ground for capital. However there is a chicken / egg issue in terms of: what made foreign capital see london as the desirable play ground? High prices. (And laws that favour the landlord.) treating property as investment increases demand and makes prices higher. Which then makes it a more desirable investment so it attracts more capital and so it goes on. Laws that restricted all this carrying on (at the expense of people who just want somehwere to live, whether they are renting or buying) would be a very good thing.
This "reluctant landlord" thing is rubbish. if you have a house you don't want to live in, you are very lucky. If you have chosen to acquire it in order to do business with it, you should be properly set up to do business according to the prevailing laws and market conditions and if these chnage, then you need to change with them. No one has a god given right for their business to be successful. If you came into the house by inheritance, it is a windfall, and it is your choice how you treat it - you can move into it, lucky you, a free house; or you can sell it, lucky you, now you can invest the money; or you can let it, if the conditions are right, but if they aren't, why should I be all boo-hoo for you?