The Green party of England and Wales has one MP, two MEPs, two London assembly members and 139 city and county councillors. Last year membership stood at 16,000. At the 2010 general election it fielded 310 candidates winning 265,243 votes. In the 2012 London mayoral election, the Green party's Jenny Jones beat the Liberal Democrat candidate into third place. Despite this very real political presence the Green party seems to be invisible to many on the left in this country. Here are a few recent examples:

• In the introduction to the book NHS SOS: How the NHS was Betrayed – and How We Can Save It Ken Loach notes the Labour party has been a key player in the privatisation of the NHS before asking rhetorically, "When people ask who they can vote for to defend the NHS, what do we tell them?"

• Writing in the Guardian, Russell Brand urged people not to vote: "The only reason to vote is if the vote represents power or change. I don't think it does." However, he ended the article arguing "I believe in change… A system that serves the planet and the people. I'd vote for that."

• In October 2013 Adam Ramsay, who describes himself as "an active member of the Green party", published an article titled, Public ownership is ridiculously popular. Why does no one campaign for it?" Ramsay mentioned the Tories, Labour, the Lib Dems, the Scottish National party and Plaid Cymru but not the Green party.

To answer these people: Ken, you can tell people to vote for the Green party because they oppose the privatisation of the NHS; in fact the Greens also want to abolish prescriptions and re-introduce free dental care and eye tests. Russell, you say you would vote for "a system that serves the planet and the people". Well, earlier this year you described Caroline Lucas MP as someone "who actually cares about things that affect us" and "is endeavouring to enact the needs of the people". Would you vote for her? And Adam, the Green party 2010 manifesto stated that they want public services "run for public benefit, not private profit. We will ... return our energy, water and rail networks to public ownership".

This invisibility cloak is frustrating because there is considerable evidence to suggest the Greens would receive much more support if they received more exposure. According to a November 2013 YouGov poll, 84% of people think the NHS should be run as a public service, 68% support nationalising the energy companies and 66% want to nationalise the railways – all Green party policy. The Greens opposed the wars on Iraq, Libya and Syria and have long called for the withdrawal of British forces from Afghanistan. A 2009 Guardian/ICM poll found 54% of respondents agreed with the Green party's policy of scrapping Trident.

All this is confirmed by the fascinating Vote for Policies website. Created for the 2010 general election the website polls people on the policies of the main political parties – without the person being polled knowing the party connected to the policy. So far 347,799 people have completed the survey, with the Green party the most popular party with 24% of the votes (Labour received 20%, the Lib Dems 17%, the Conservatives 15%, UKIP 12% and the BNP 10%).

Of course, the UK's first-past-the-post voting system doesn't help, with influential commentators like Owen Jones arguing that voting Green is effectively a wasted vote. This kind of defeatist thinking would have been disastrous for the nascent Labour party in the early 20th century. How would it have grown to become a force for progressive change if voters chose the least bad option in the 1906 general election (the Liberal party) or decided not to vote for Labour because they only had two MPs at the time? As per the invisible rule, Jones himself rarely, if ever, mentions the fact that his own politics often have more in common with Green party policy than they do Labour – such as the Green's strong opposition to austerity and their proposed Green New Deal solution.

Despite all this, things seem to be looking up for the party. A November 2013 Ipsos Mori opinion poll found 7% of respondents said they would vote Green if a general election were held tomorrow – just 1% behind the Liberal Democrats and Ukip. This hopeful result came on the back of a You Gov poll that found 12% support for the Green party in European election voting intentions – in front of the Liberal Democrats on 10%. If followed through in the May 2014 election this result would likely treble the number of Green MEPs to six.

How long will the left continue to ignore the parliamentary party with the most progressive and radical policies?