This is not false but the majority of people and properties are freehold, not leasehold. Around 3 million properties are leasehold, the majority are flats, with 1 million being houses. There are about 25 million residential properties overall, so leasehold is only about 12% of the market.

Plus, in the UK there are certainly liabilities for holding land that has a residential property on it. As the landowner, you'll be paying the council tax on it if you have no tenants, and with many councils now, that'll be a more expensive rate too (currently 150% of the standard rate for unoccupied property in my area). Of course, council tax isn't really a property tax, though it can act like one in some situations and basically covers similar things that US property taxes do.