This is certainly a tusk of some sort but whether it is from a mammoth or another species is less clear. If this is from North Kent (in the general area of Herne Bay) there have been a number of such finds made recently at the lowest tides - some of them are on display in Herne Bay Museum. They are of the extinct straight-tusked elephant, of last interglacial age, rather than mammoth of the last glaciation. This find could be similar.
So, if you are in the Herne Bay area, as a first port of call it may be worth taking your photo (or the find itself) to the museum to see how it compares to their specimens.