I also moved there from London, OP, from a tiny central London flat when circumstances meant it was no longer practicable for us. We both worked in the city centre in Leicester.
Leicester is culturally diverse, it's true, in terms of there being lots of different ethnicities living broadly unproblematically side by side, but if by that you also imply cultural diversity in terms of lots of interesting stuff going on under the umbrella of 'culture', I found that not to be the case. On the up side, you could get wonderful Asian food, and things like Diwali and Holi were often fun, and there are some gorgeous Arts and Crafts houses, and an annual comedy festival.
On the other hand, there was only one main theatre which did only a couple of original productions annually, and seemed to mostly have touring musicals, a couple of small museums (and the Richard III visitor centre!), very little live music of any kind, no decent bookshops, and not much of a cultural scene in general -- and if you are relying on being able to nip back to London for gigs/theatre, the last fast trains back to Leicester leave St Pancras very early, and the later ones can take the best part of two hours rather than just over one. The city centre feels quite run down, and has been wrecked by bad development, dominated by the Highcross shopping centre, but with lots of empty shops, or spaces occupied by charity shops or pop-ups, on the actual streets.
I'm not from the UK originally, but have lived in several different parts of it, and I've lived in much smaller places with far more going on.
The other thing I found difficult (which may of course not bother you at all) was being so far from the coast -- it's a good two hours or more in the car, and rather more to get to nice beaches, and there was something kind of mad and desperate about the way people flocked to Rutland Water in hot weather. East Leicestershire has some pleasant, rolling countryside.
I would agree with @CarHire101's suggestion of Birmingham as far preferable, if you need to be in the Midlands.