I have no wish to intrude on the Labour leadership debates and I have no idea whether former shadow health minister Heidi Alexander is right in her critique of Jeremy Corbyn’s leadership style, but for her aides to pick out Corbyn’s support for my NHS reinstatement bill as evidence both of his “ineptitude” and of his shadow chancellor’s “undermining” her strikes me as both desperate and depressing (Shadow cabinet inept and shoddy, says MP, 20 August). My private members’ bill, drawn up after extensive consultation with health experts and health service users, would have reversed the creeping marketisation of the NHS – under both New Labour and the Conservatives – and stripped away the costly market mechanisms that waste NHS money and lead to inefficiencies and the fragmentation of services.

Perhaps a more interesting question is why the rest of the Labour party didn’t join their SNP, Plaid and Lib Dem colleagues in giving it their backing too. With a few honourable exceptions, they chose to abstain instead. Yet this is precisely the kind of policy a successful Labour party would surely be expected to promote – as well as demonstrating a greater willingness to work alongside colleagues from other parties on those areas where there is common ground between us.

Overcoming party tribalism and finding practical ways of working together will be crucial to any hope of progressive policies finding a majority at the next election – whether that be on the NHS, tackling inequality, putting rail in public hands, or seriously addressing the climate crisis. Real leadership means being bold and honest enough to recognise that there’s far too much at stake to refuse to cooperate for the common good.

Caroline Lucas MP

Green, Brighton Pavilion

• Heidi Alexander’s self-justifying piece would have made David Brent blush. Alexander had perhaps the easiest job in Labour front-rank politics – defending a properly funded, publicly run health service free at the point of use – yet she managed to reduce her portfolio to dull, uninspiring managerialism. On every count she flings at John McDonnell for “undermining” her – his joining a junior doctors’ picket line, his gathering the views of frontline health activists and his support for Caroline Lucas’s NHS reinstatement bill - McDonnell clearly spoke for the vast majority of Labour supporters and members.

John Medhurst

Hove, East Sussex

• Jeremy Corbyn’s support for a National Education Service is welcome but hardly “courageous” (Zoe Williams, 15 August). None of his statements to date have spelt out the urgent reforms needed to England’s segregated and hierarchical system of secondary schools. He could confront the need for an integrated 14-19 curriculum and discuss the future of the GCSE. He could propose new forms of local and regional accountability. He could discuss fair admissions, measures to reduce religious segregation and how to end, not extend, the 11-plus. Without more detail Labour’s policy on secondary schools will, sadly, remain an empty space. Even more courage is needed, Jeremy.

David Chaytor

Todmorden, West Yorkshire

• It is a sad day for British democracy that Momentum – the left-wing ginger group active within the Labour Party – has seemingly turned its back on non-violence (Momentum no longer rules out acts of violence, 20 August). Momentum’s unwillingness to sustain its previous principled opposition to violence is because some of the fringe groups who are associated with them want a licence from the left to face down neo-fascist groups fist-by-bloody-fist. Aligning this sort of macho political posturing with what the brave men and women who resisted the Nazis did is an insult.

Martin Jones

New Barnet, Hertfordshire