Figures from the 2001 census for Yorkshire and The Humber are available on the CRE website in a fairly straight-forward format. For example:

Yorkshire and The Humber ranks fifth of the nine English regions in terms of its proportion of ethnic minority residents. About one in 12 people living in the region are from ethnic groups other than White British. In 2001, 4.7% of people living in the Yorkshire and The Humber were born abroad, up from 3.7% in 1991.

Out of every 1,000 people, on average:
* 916 are White British
* 45 are Asian
* 18 are White non-British
* 9 people are of mixed race
* 7 people are Black
* 2 people are Chinese

It's also possible to get figures for Leeds, Sheffield, Bradford, Rotherham, Barnsley, Doncaster, York, Harrogate and Hull.

I'm not sure how long they have been available there but it seems as if it is only fairly recently.