When MPs from different parties put aside their differences to work together, it’s worth listening to what they have to say – especially when it comes to protecting our crisis-ridden NHS. So when Liz Kendall, Norman Lamb and Nick Boles took to the airwaves this morning proposing a cross-party solution to our healthcare crisis, I understand why many people will have listened with interest.

I agree with a number of the proposals, including a commitment to keeping the NHS free at the point of use, integration of social care and increasing funding above inflation. But sadly – and I don’t doubt these MPs care about the NHS – I believe that the sum total of their “ten principles of long-term funding for NHS and social care” ​risk undermining healthcare in this country.

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Before examining the proposals themselves, it’s worth taking a slightly closer look at the “cross-party” nature of these proposals. Both Norman Lamb and Nick Boles were ministers in the same coalition government, and Liz Kendall is firmly on the right of her party. It’s fair to say their recent politics are fairly aligned. Perhaps it’s this political alignment that caused this group to fail to mention privatisation at all in the proposals – indeed both Boles and Lamb supported the privatising 2012 Health and Social Care Act, and Kendall is on the record as a defender of private sector involvement in the health service.

Without a mention of the damage of privatisation, or any commitment to reverse it, I fear that these proposals risk becoming a vehicle for companies to further profit from the fracturing of the NHS. There is no solution to our NHS problems that continues to allow the likes of Virgin to sue our health service, or to end the chaos, cost and waste of fragmentation.

I don’t just fault these proposals for what they fail to mention – I also believe that their central suggestion, a hypothecated tax for health and social care, is extremely risky. The first risk is that such a tax would not raise the amount required, and we would have to rely on the goodwill of the Treasury to top it up anyway. As Paul Johnson, the head of the IFS, says, a spending stream that relies mostly on wages risks seeing serious reductions during economic downturns. Would we expect less money for the NHS during times of wage stagnation?

The second major risk of a hypothecated tax is that it undermines the very concept of general, progressive taxation – and further entrenches the view that healthcare is entirely about treating the sick, rather than keeping people well. Public spending in all departments can contribute to people’s health: whether it’s local authorities investing in sports centres, social security being kept at a level that allows people to afford to eat healthily or every child being given an equal start in life through world-class education.

A look back at the groundbreaking Marmot review of health inequalities reminds us that tackling ill health is about much more than just funding hospitals, and that doing so will actually save the government money in the long term.

When you take out the popular parts of public spending from general taxation, only the less popular parts are left, thus potentially giving the government more political space to cut back on welfare, education and other spending. We’ve already suffered eight years of budget cuts, and as a result have record numbers of people relying on food banks to feed their families – leaving it abundantly clear to me that we should not risk giving the government further opportunity to attack the state.

With swaths of evidence ​showing that more equal societies are healthier, surely a more progressive alternative to a hypothecated tax is for politicians from across the parties to stand against the reckless ideology of austerity and for significantly higher taxes.

I know that politicians from all sides are desperate to fix the NHS crisis. But by ignoring the marketisation of the NHS and focusing instead on how we raise taxes to pay for the NHS, Boles, Lamb and Kendall pick the wrong structural problem. There is nothing wrong with general taxation, and a debate about hypothecated taxes is a useful way, not least for Tories, to avoid admitting this government’s gross underfunding and mismanagement.

We cannot go on with people being treated in hospital corridors, and waiting times ​at our A&E departments increasing month after month. But we must also be honest about the fact that there is no solution to our NHS crisis that doesn’t involve repealing the dreadful Health and Social Care Act of 2012, which risks giving government carte blanche for policies that undermine the very health of the nation. I’d urge MPs who are passionate about protecting our health service to support an NHS reinstatement bill​, which would roll back the years of marketisation and put us on a genuinely secure footing for the future.

• Caroline Lucas MP is co-leader of the Green party