The 2011 Census data has been released for the travel to work question.
The Guardian have done a nice job of turning the data into maps, and amongst it it is possible to see the Manchester area cycling data.
I've done a screen grab of the key part of Manchester.
The pale areas are in the 0-5% range whilst the blue areas have a 5-10% cycling share of journeys to work.
You can quite clearly see how the south-west of Manchester has the big concentration of people who cycle to work. Note that this probably does not include the student population cycling to university or college, so the actual level of cycling in South Manchester is higher and more widely spread.
Also, as far as I can tell these are the uncorrected percentages which include people who do not work, the figures would be higher if they were excluded.
If you go to the Office for National Statistics web site you can find the source data by local authority area.
Gtr Mcr 37.8 1.3
Bolton 40.3 0.6
Bury 43.3 0.9
Manchester 25.1 2.3
Oldham 38.0 0.6
Rochdale 38.6 0.6
Salford 35.0 1.5
Stockport 43.7 1.4
Tameside 39.7 0.9
Trafford 43.4 2.1
Wigan 44.0 1.0