The Protection from Eviction acts protects you from eviction without due cause until the end of the tenancy (based on my reading of it).
The problem is that here in the UK, many tenants, including myself, are on rolling month to month tenancies. Meaning that every month the landlord gets to decide whether or not he wants to keep me as a tenant.
Very different from my experience in NYC, where leases are one to two years long and are renewed automatically unless the tenant wishes to leave or there is cause to evict the tenant (e.g. for non-payment of rent, intolerable behaviour, etc.)
I agree that in the US, a rented apartment feels like home. Back in NYC, people grew up, married, had kids and grew old all while living in rentals. Here in the UK, renting seems to be seen as a temporary situation, for young people just out of school until they can afford a downpayment on a home, or perhaps for someone who is just divorced and needs some time to get their finances in order.
The flat I live in now is actually larger and in a nicer area than my last apartment in NY. But I felt much more secure there than I do here.