Mate, you began this entire thread with the intention of dragging the council through the dirt on this because you had yourself confused.
When challenged on your assumption that the council pay for this provision, you said 'they do pay.got it in writing.'
Just to be clear, your council tax stays in the city - that's law. Just as it's law that a council cannot make a profit. Council tax contributes to nothing beyond the confines of the respective council's zone and subsequent responsibilities. Council tax does not pay a thing towards Beryl Bikes. Tax coming from central government is used, but that's 100% not council tax.
Again, you have yourself confused.