The council represent you. If there was enough will, they would have no choice.
I wouldn't vote for Labour (or, LibDem and I'd never vote Tory, never ever ever!).
When I do vote, I won't vote on policy for CCFC, I vote on issues like tax, NHS, economic policy, etc. etc. national issues, not a small time stadium in Coventry, and most people don't vote for their MP, they vote for the party on the national stage (one reason of many I don't like FPTP) so no, I reject that notion.
The council nor state should have no business with regards to running clubs nor their stadium, nor backing up a private company that runs the ground! The only responsibility they have is funding the FA to increase Grass Roots participation etc.
My step-dad (Millwall fan) said to me a couple of years ago, when I was younger and even more naive, that I'd be silly to think the council would sell the stadium to CCFC, he was right. The CCC will say use HR as an example (what did we actually do wrong? I genuinely don't know) but it's got nothing to do with that, all they're interested in is the money, profit, New Labour has betrayed its Socialist founding principles and it stinks.