The more recently-released Census results distinguish between built-up areas and local authorities, and the results can be startlingly different indeed when you exclude the rural areas that are included in some cities' local authorities. Here is a sample:

Bolton Local Authority: 20.1% Asian, 3.8% Black, 2.2% Mixed-race, 71.9% White, 1.9% Other.
Bolton built-up area: 28.4% Asian, 5.1% Black, 2.4% Mixed-race, 61.6% White, 2.5% Other.

Bradford Local Authority: 32.1% Asian, 2% Black, 2.7% Mixed-race, 61.1% White, 2% Other.
Bradford built-up area: 45.3% Asian, 2.9% Black, 3.2% Mixed-race, 45.8% White, 2.8% Other.

Doncaster Local Authority: 2.9% Asian, 1.2% Black, 1.5% Mixed-race, 93.1% White, 1.2% Other.
Doncaster built-up area: 7.3% Asian, 2.7% Black, 2.3% Mixed-race, 84.4% White, 3.2% Other.

Dudley Local Authority: 8.4% Asian, 2.5% Black, 2.8% Mixed-race, 84.9% White, 1.4% Other.
Dudley built-up area: 17% Asian, 6.4% Black, 4.2% Mixed-race, 70.4% White, 2% Other.

Oldham Local Authority: 24.6% Asian, 3.4% Black, 2.5% Mixed-race, 68.1% White, 1.4% Other.
Oldham built-up area: 43% Asian, 5.3% Black, 2.9% Mixed-race, 46.4% White, 2.3% Other.

Rochdale Local Authority: 18.5% Asian, 3.5% Black, 2.4% Mixed-race, 74% White, 1.6% Other.
Rochdale built-up area: 34.3% Asian, 3.4% Black, 2.5% Mixed-race, 57.2% White, 2.6% Other.

Rotherham Local Authority: 5.3% Asian, 1.1% Black, 1.4% Mixed-race, 91% White, 1.1% Other.
Rotherham built-up area: 15.5% Asian, 2.2% Black, 2% Mixed-race, 77.5% White, 2.8% Other.

Wakefield Local Authority: 3.6% Asian, 1.3% Black, 1.4% Mixed-race, 93% White, 0.7% Other.
Wakefield built-up area: 9.8% Asian, 2.8% Black, 2% Mixed-race, 83.7% White, 1.8% Other.

Walsall Local Authority: 18.7% Asian, 4.6% Black, 3.3% Mixed-race, 71.4% White, 2.1% Other.
Walsall built-up area: 47% Asian, 6.9% Black, 3.5% Mixed-race, 38.1% White, 4.5% Other.