The government’s offer to include new commitments on workers’ rights in Brexit legislation is part of a political equation that looks simple enough. The prime minister needs votes in parliament for her EU withdrawal agreement, dozens of Conservatives say they are opposed and some Labour MPs representing leave-voting areas are amenable to a deal. But they need reasons to back one.

A guarantee that workers’ rights will not be shredded on the way out of the EU would help to satisfy some opposition reservations about the project. Labour MPs dislike Brexit for many reasons, but they are especially allergic to the hardline Eurosceptic ideology that sees workplace protection as a menace to enterprise and liberty. Theresa May is not an orthodox disciple of that school. She claims to be a willing guarantor of benefits that evolved under EU membership.

The newest expression of that claim is a plan to give parliament rights to resist a post-Brexit “regression” from European standards. Greg Clark, the business secretary, on Wednesday told the Commons the government would have to show that new laws will not corrode old rights. MPs would also have the opportunity to consider any future improvements in worker rights at a European level and imitate them with British statutes.

This is a tiny upgrade to powers that already exist. If there is a Commons majority for a new regulation, some way to introduce it can surely be found without Mr Clark’s clauses. The government is offering Labour MPs a gesture of readiness not to fall behind EU standards, not a locking device that keeps the two regulatory regimes in step. Mr Clark rejects the idea of automatic alignment on the grounds that it would outsource power to Brussels and so negate the purpose of Brexit.

That is the nub of the problem. Labour MPs do not trust Conservatives to implement a Brexit that respects social protections, and the Tories cannot win that trust because most of the party does indeed see divergence from European social norms as a motive for leaving the EU. It was never plausible that a bridge could be built between those positions, but the prime minister’s dismal attempt says something about how desperate and narrow her political ambition has become. Her current interest in protecting workers’ rights is tactical. It is part of the daily scrabble for a majority. That motive is at best tangential to the good reasons for wanting well-regulated labour markets, which is to resist exploitation and a race to the bottom in terms of pay and conditions.

The relationship between Brexit and labour rights is not simply a transactional question of what Labour MPs will take in exchange for supporting a deal. It is a question of the social and economic conditions in some parts of the country, epidemic job insecurity, and feelings of political and financial neglect that drove millions to crave a drastic upending of the status quo. The challenge in those areas is not to nudge the local MP into an aye lobby to deliver a Brexit deal but to understand and address the underlying grievances that were expressed in the referendum result.

There was a time when Mrs May’s promises to tackle those issues deserved a hearing. Her conservatism is not of the sink-or-swim variety that once treated economic decline in some communities as a market correction, best allowed to run its course. But she has lacked the authority among colleagues and the political space to develop a more compassionate agenda. EU negotiations have consumed her time in office and, beyond the one-off gratification of saying it has been done, Brexit promises no remedy for the anger and disillusionment that compelled many people to vote leave.

EU membership was not the cause of the ailment so losing its economic advantages is no remedy. If the government had demonstrated a meaningful shift in its understanding of Labour MPs’ concerns and the value of workers’ rights, it might have been said that the last-minute hunt for votes in parliament had yielded a long-term benefit. Instead, ministers are offering a concession so small it cannot cover the cynical motive behind it. This is shabby politics, poorly executed.