In my experience it was moderately diverse relative to a lot of other unis in the south. Also worth bearing in mind as Southampton itself is reasonably diverse, and also as a major port city has a lot of people of different backgrounds and ethnicities coming through the city for a day (i.e. the seafarers from the ships, who may end up taking shore leave in the city).
I think comparing to London is a bit challenging because there really are few cities as diverse as London in the UK outside of other major metropolitan areas like Birmingham/Manchester etc. Smaller cities invariably end up somewhat less diverse, but compared to others I've lived in (e.g. Exeter, Cambridge) I find Southampton seems somewhat more diverse on average relative to its size.
In terms of the census, Southampton is 10.6% Asian or Asian British (compare with London 16.8%, Cambridge 14.8% or Exeter 4.9%), 3.3% Black, Black British, Caribbean or African (compare with London 2.7%, Cambridge 2.5%, or Exeter 0.9%) and 3.3% mixed or multiple ethnic groups (compare with London 5.5%, Cambridge 5.1%, or Exeter 2.5%). Notably also in terms of the white population, 12.6% are white other (i.e. not white British).
So I'd not consider it to be a not multicultural city - compared to places like London or Cambridge which are considered quite multicultural it is not far off, and considerably more diverse than some other small regional southern cities like Exeter. As I recall the university itself also has some pretty active Asian and Afro-Caribbean societies too?