Hi Agis
I cannot give you a definitive answer as I do not have enough information.
You can check by putting your information into one of the online benefit calculators.
gov.uk/benefits-calculators If you move local authority areas then you will have to apply for UC. Housing Benefit is not dependant on claiming PIP but you may be eligible to get additional premiums depending on your circumstances. If you move within the same local authority area and there is no change in your circumstances, then you should stay on housing benefit.
The SDP gateway ended on 27th January 2021. From that date it has not been possible for single working age people to make a
new claim for HB (except if it is in respect of specified or temporary accommodation).
A claim for UC will bring any Income Related ESA to an end. But if you receive CB ESA then this will continue (and be taken into account as income in the UC assessment).
Gary