Tenancies in the UK are governed by the tenancy agreement between landlord and tenant and the relevant legislation.
At the time of writing, a landlord may increase the rent at the start of a new tenancy without limitation. Within an active tenancy, changes to the rent will either be prohibited or likely limited in some way.
In our blog: 'London Rent Prices Over the Last Decade', we looked at the changing rental values across England and Wales over the last ten years.