Of course private rental btl's have driven up house prices and of course landlords are richer than tenants.
To take the latter issue first, landlords own. They have assets. Not all wealth is seen in the bank - we need to get out of the mindset that money on a banksheet is all and resources are irrelevant, here and elsewhere. Tenants do not own. Tenants have nothing more in many cases than the clothes in the (landlord's, often) wardrobes. This is a huge discrepancy and it is nothing more than facile duplicitous lies and hypocrisy that enables the rich to overlook it.
For the first issue, let's pretend you have ten houses and ten families. Everyone has one each, no problem, prices are normal. One family, being older, pays their mortgage off earlier and decides to leverage their sudden wealth and become a btl landlord. Now there are ten houses and eleven wanting them. Prices go up to satisfy demand, the first family can still afford it, the youngest can't and become tenants with no assets. Next, the second oldest pays off the mortgage. Now we have ten properties and twelve families wanting to own. Prices go up.
Do you see when it is laid out like that? Of course the greed of landlords drives up prices for everyone. It is very simple, supply and demand. The way the well-off have been trying to pretend it isn't happening and that they are not simply leveraging their excessive prior-earned wealth at someone else's expense has been sickening for years.
The multiple ways in which the well-off in a society can leverage prior wealth to force all poorer people into poverty have been well understood for years. It happened in Britain in the Victorian Age (even if we didn't have numerous examples in the ancient world and ancient laws against usury to draw on). The public sector was one compromise that worked well against until it started becoming corrupted. We need it back, and we need systemic guards against it becoming corrupted again.