As I said on the other thread, local action needs to be taken. Decisions about library services are made by local councillors and you need to appeal directly to them. What matters to local councillors is re-election so a local campaign to save our libraries will make them realise what it is the best interests of their constituents. 
What mumsnet could usefully do is lobby nationally and co-ordinate a campaign, perhaps by supplying resources for local people to use?
Fundamentally it comes down to use them or lose them. Sadly some local libraries are very under-used and these will be at risk.
Councils have a statutory duty to provide an effective library service so it might be helpful if Mumsnet (or a clued up Mumsnetter) could provide us with guidance on what this means so that Councils can be challenged on this basis?