This article, from Wednesday's Guardian, is highly relevant and the policy (RA405) adopted at Spring Conference this year states our support for the rights of migrants to healthcare regardless of status:
RA405 The Green Party will oppose any person being left destitute after a failed asylum claim or if deemed to have not applied "appropriately". Any person in the United Kingdom should be entitled to the basic necessities of life, including but not limited to food, shelter and medical care, by legal means, whether this be achieved through employment rights or public funds.
Moyra Rushby, quoted in the article, spoke at a well attended fringe meeting held by GPTU on migrant workers at that conference.What is happening (as given in the example near the end) is truly inhumane treatment by the NHS of vulnerable people who suffer because of a system that is chronically underfunded. It is a small step from this to the idea that 'if you haven't put into the box, you aren't allowed anything out'. If undocumented migrants can't get healthcare while they remain in the UK, why should someone who has never paid taxes? Once healthcare is not seen as an inalienable human right, we are on a very slippery slope indeed.