The Regs
New government regulations of August 2020 allow extra storeys to be classed as ‘Permitted Development’ meaning you don’t need planning permission.
In order to qualify your house must have been constructed between 1st July 1948 and 5th March 2018. Two storey buildings and above are able to go up two additional storeys and a one storey building is able to go up one storey only. There is a limit of a total building height of 18m.
Other restrictions include that the new roof pitch must match the existing and finishing materials – bricks, tiles, windows - must match the existing.
From www.legislation.gov.uk:
Permitted development
AA. The enlargement of a dwellinghouse consisting of the construction of—
(a)up to two additional storeys, where the existing dwellinghouse consists of two or more storeys; or
(b)one additional storey, where the existing dwellinghouse consists of one storey, immediately above the topmost storey of the dwellinghouse, together with any engineering operations reasonably necessary for the purpose of that construction.
The full regs can be found here: https://www.legislation.gov.uk/