Can you really believe it's the Conservative Party that has afforded so many Prime Cabinet Posts to non-Caucasians ?
Logic says it would be Labour ( certainly not the virtually pure-white Lib Dems) but reality means an Asian Chancellor and Health Secretary.
On the face of it The Conservatives appear to be more multi-cultural than the other Big Parties.
Firstly, I would give credit to David Cameron, He spent time in opposition modernising the party, 'encouraging' a wider range of candidates on reluctant constituent parties. He did for ethnic diversity in the Conservatives, what Blair did for gender diversity in Labour.
I would also add that the advancement of ethnic minorities into cabinet has only really happened under Johnson (only Javid and Patel predate him). It may be on this Forum or elsewhere that claims have been made than Johnson wants ministers who are less 'talented' than himself; I actually that he wants ministers who are grateful to him. Williamson and Patel given a second chance, some lurking towards the right fringes of the party might think their views would exclude them, but others who might have been overlooked under previous leaders or potential leaders - and this includes some who Johnson has now advanced.
Labour - 2002 Paul Boateng was Chief Secretary to the Treasury (Brown's no 2), 2003 Valerie, Baroness Amos was Secretary of State for International Development (first BAME woman to be a cabinet minister), 2007 Patricia, Baroness Scotland was Attorney General. Labour has got a lot more to do but the roots had been set down. Of course, Labour hasn't been in power since 2010 so the current crop could not qualify; Chuka Umunna would have be pretty certain of a post in 2015 if Labour had won.
One last, controversial element, I'm not certain whether Labour is helped by our system of having ministers who are the people's representatives. There seems to be a fair share of BAME members who are/ had been either towards the left edge of the parliamentary party or appear to be content to represent their constituents (no problem with that, that is why they were elected) or to campaign on particular issues.