Do waste water pipes for kitchens and bathrooms require a minimum slope to avoid clogging?
I am not in the UK but my city uses the International Plumbing Code.

Everything needs to have the required slope. The required slope depends on the size of the pipe.

IPC table 704.1 shows that a pipe with an ID (interior diameter) of 2.5" or less needs 1/4" per foot. While a pipe that is 3" to 6" only needs 1/8" per foot.