Hi OP!
I'd suggest the Trafford area (Sale, Altrincham). I'm South Asian (mostly).
Altrincham is one of the few areas in the rest of the country that has 'London' house prices but we're talking the outer zones not Central. You can get a lot for your money. 30 min tram to Manchester for everything you want. Dunham Massey park, the Altrincham market sells great produce and there are other smaller farms (not farmers markets. actual farms) 10-15 minute drive away.
There are lots of shops and cafes in the vert walkable town centre nearby there's also Disbury. Indepdent butchers, greengrocers etc etc all very acessible. There are also quite a few Caribbean food shops in Stretford! Timperley has an Indian grocer
No city in the UK is equal to London. The latter's not just a big city, it's a metropolis. However, you have museums, National Trust sites etc easily accessible across the whole of the NorthWest from Manchester. if you were going to live an hour away from London. Which would arguably mean you take 1.5 hours to get anywhere ( train in + tube/bus to the actual attraction.).
There is nothing stopping you from doing the same by going to Manchester and then to Leeds, Liverpool, etc.
Altrincham area is very diverse thanks to the big Barclays Tech Center that recruits a lot of young graduates, ethnically diverse people, internationals etc. Most don't want to stay in Knutsford so choose the Trafford area. There's been an influx of Hong Kong migrants as well.
Despite people claiming the 'diversity' of other places, St Albans etc is NOT more diverse than Altrincham. 2021 census:
St Albans:
https://www.hertfordshire.gov.uk/media-library/documents/about-the-council/data-and-information/equality-and-diversity/equality-and-diversity-profiles-st.-albans.pdf
Trafford:
https://www.traffordjsna.org.uk/Life-course/Start-well.aspx
The second is kids, the first is all adults but I'd expect the figures to not differ so wildly neither are the sort of place where one family has a lot of children.
I'm South Asian (with SEA and Black blood as well from my great grandparents). I moved out of London because it was too big and busy for me. Sadly I couldn't afford to buy in Altrincham either (one day!) and moved elsewhere but for your budget it won't be an issue. The North West is great.
I'm so annoyed at people proclaiming that anywhere outside of London has diversity issues, just go on a night out in manchester or liverpool! There are loads of us here. A lot of people tried to scare me from moving but I'm glad I did... my bank account is laughing while they're still stuck paying London rents thanks to the fear. And I earn a good salary too.