No.
Biodiesel is fuel made directly from vegetable matter; typically it needs a ""special"" engine to run, or is blended in a low ratio with ordinary diesel (B7 in the UK and EU).
Processed cooking oil is made into HVO.
This can be used as a direct 1:1 replacement for ordinary diesel without engine modifications. Very green! Unsurprisingly, HVO has a higher price than biodiesel.
https://en.wikipedia.org/wiki/Hydrotreated_vegetable_oil
HVO is easily available in the UK and is typically bought by bus companies and delivery companies seeking to improve their green footprint.