Imagine being in government (a wistful thought for many readers of this blog, I know) and having a device that forced the main opposition party to take responsibility for your most unpopular policies. Not just a rhetorical flourish that enabled you to blame the previous government, but a mechanism that meant that, day-by-day, your opponent had to be the face of cuts to people's most valued services. The Conservative government has exactly such a device: it's called local goverment, and all over the country it is pushing local Labour parties into a confrontation, both with service users, and especially now in the era of left-wing influx, with party members and trade unionists.

This coming Monday, Unison members in Lambeth will go on strike in opposition to major cuts to local library services, including a plan to turn three libraries into gyms, causing redundancies and a loss of capacity in what is already an overstretched service. For the council, the reduction in library services is unfortunate but necessary. But staff have voted with an 88.5 per cent mandate to strike. The cuts are, according to Lambeth Unison branch secretary Ruth Cashman, “nothing short of cultural vandalism”.

The Tories' use of local government cuts to hit Labour-controlled areas is not new. In the mainstream commentariat, it has become the norm to blame the big stand-offs between the Thatcher government and local councils like Liverpool on the hard left, in part because this narrative is one of the founding myths of New Labour. But they were in large part a result of a deliberate policy of underfunding, rate-capping and removal of powers from local authorities. That policy continues today: many deprived Labour-controlled councils like Lambeth are set to face cuts more than ten times harsher than those imposed on leafy Conservative-controlled councils.

Disputes like those over Lambeth's libraries go to the heart of what Labour is for. For Jane Edebrook, the councillor responsible for the libraries policy, the cuts are simply unavoidable given the scale of central government cuts and “the fact that we spend more than 50 per cent of our remaining budget on the 10,000 most vulnerable adults and children in the borough”. Cashman, who is herself a Labour activist as well as a trade union rep, points out that there are 16 council officers on over £100,000 per year, and another 19 agency staff in the same pay bracket. “I will not be lectured”, she says “on libraries versus children’s social care when holding a pay report signed by 16 officers who each individually earn more than the entire budget for children’s books across ten libraries”. In Labour wards and CLPs in the local area, motions have been passed condemning the cuts and supporting Lambeth Unison.

The internal crisis provoked by budget cuts is not limited to Lambeth. Two weeks ago, the Labour group on Haringey Council suspended one of its councillors, Gideon Bull. Bull's offence was to speak out against the closure of local day centres for adults with dementia and disabilities in a Cabinet meeting. Tottenham CLP has formally condemned Bull's suspension. Since the Tories came back into power, there have been a number of episodes in which Labour councillors have rebelled against the whip on cuts in Southampton, Nottingham, Sunderland, Hull and elsewhere. Most have faced disciplinary action or been pushed out of the party altogether.

Even on the left of the Labour Party, the idea of setting illegal budgets and refusing to implement central government cuts is controversial. Just before Christmas, the new leadership penned a letter to council leaders clarifying that they did not support the idea – and although their objections were tactical rather than ethical, this does mark a significant change for likes of John McDonnell, who publicly supported the tactic in the 1980s. Nonetheless, the scale of cuts being funnelled through local government presents a serious danger to Labour, especially under its new anti-austerity leader.

“The answer from Lambeth's trade unions,” says Ruth Cashman, “is fight with us. They say 'we have to do the responsible thing' – but when Labour councils did the responsible thing, the government thanked them by making even deeper cuts. It is not responsible to sell off your libraries, or to dismantle services which save lives and make life worth living.” Although the law now makes it much easier for central government to take over where councils set illegal budgets, doing so could, say activists, still be a viable strategy for defeating cuts – if Labour's councils got on board, prepared well, and jumped at the same time. The problem is that they almost certainly won't. Many Labour councillors are committed to the idea of a balanced budget, and the political culture in many Labour groups means that dissenting voices are often silenced.

Whatever happens, if Labour is to be a credible anti-austerity party, it will have to develop a serious anti-cuts strategy in local government. That might not immediately involve setting illegal budgets, but it must certainly involve council leaderships respecting the will of trade unions, party members and the communities they represent. Otherwise, the Conservatives will get what they want: a Labour Party that fights itself and cuts your local library.