What should happen to the EU citizens who came to the UK before Brexit? In theory, the answer should be simple: both sides in the referendum campaign, as well as large majorities of leave and remain voters, believe that their rights to stay in the UK should be protected. Which raises two questions: should their right to stay be guaranteed by the UK unilaterally, in advance of a deal with the EU on reciprocal rights for UK citizens in the EU? And how exactly would this right apply in practice?

Last autumn, the NGO British Future set up an inquiry to make the case for a unilateral guarantee, and to look into the details of how it should work. It was chaired by Gisela Stuart, the Labour MP who strongly supported the leave side in the referendum, and the panel included people from both sides of the Brexit debate, including me.

I agreed to participate because, as a specialist in EU free movement law, I thought I could help with some of the legal detail we were looking at. Also, as a remain supporter, I thought that it was a good idea for those on the two different sides to work together on an issue we could all agree upon, rather than continue to be divided. In particular, I thought that Stuart would do a good job making the case for a unilateral guarantee.

The report of the inquiry, which came out in December, indeed argued for EU citizens’ rights in the UK to be guaranteed unilaterally, while seeking a reciprocal deal on UK citizens in the EU. It also recommended how to accomplish this in detail – for instance, by waiving the rules that make it hard for many EU citizens married to UK citizens to get permanent residence status.

Gisela Stuart chaired the inquiry well, and initially did a good job advocating its findings in public. For instance, she told one newspaper that “Britain should make the first move to demonstrate goodwill”. So far, so good.

But on Wednesday night, she bottled it. She voted against an amendment to the Brexit bill – tabled by her own party – that would have guaranteed those rights. (So did Suella Fernandes, a Conservative MP who also participated in the British Future inquiry).

There’s little point to an inquiry chair who votes against the policy she agreed to advocate. Moreover, she had no good reason for doing so. The amendment would not have blocked Brexit; rather it would have guaranteed EU citizens’ rights separately from triggering article 50. Leavers didn’t like the idea of amendments to the bill, but they could have made a principled case for this one, as a single exception to their rule.

Although the home secretary offered assurances on this issue that satisfied some potential rebels, they should not have sold their votes so quickly. Those assurances don’t extend to a unilateral guarantee for EU nationals; they’re just a vague promise to table a bill of some sort in the future. This means that EU citizens face many months more uncertainty. So do their employers, as Séamus Nevin of the Institute of Directors (who was also part of the inquiry) has pointed out.

If there’s one thing people don’t like about politics, it’s two-faced politicians. MPs who support a policy should simply vote in favour of it, not against it – in particular if they have chaired an inquiry advocating that very policy. There’s still time for Stuart to do the right thing. Hopefully, the House of Lords will insist on an amendment on this issue, giving her the chance to execute a graceful U-turn. If not, there’s that future bill some day.

For my part, if the inquiry were reconvened for whatever reason, I wouldn’t serve with her again and be a figleaf for her nakedly cynical tactics.