If popularity is measured in mountains of aluminium ladders, union flags, television cameras, bunting, and more ladders – all faithfully disseminated in further mountains of newsprint and website live feeds of closed doors beginning (as the Telegraph's proudly proclaims) at 4am and ending at 11pm, then the monarchy, right at this moment in silly season, appears to be unassailable. And the polls seem to bear this impression out: Ipsos Mori found this week that 77% of Britons wanted Britain to remain a monarchy, while just 17% wanted a republic – this despite the fact that the week also saw a member of a royal household hauled before the public accounts committee to show why it paid no tax on its (very lucrative) business interests. The Duchy of Cornwall, said William Nye, Prince Charles's private secretary – giving Donald Rumsfeld a run for his money in the department of obfuscatory clarifications – is "a private estate, like a private estate, but in many respects is not a private estate. But that does not make it, per se, a corporation." The percentage of people who thought Charles should give up his place in the succession actually dropped, by one point; 52% think he should keep it.

And yet, insists Graham Smith, chief executive of the campaign group Republic, and the man who might well have the distinction of being the only person in Britain who works full-time to overthrow the monarchy, "we've never had it so good". The polls, he says, have remained static for years: what is more important, according to him, is to see that that 77% support for the monarchy is "very superficial – most of those people aren't particularly interested – they are open to persuasion. We find this when we go out leafleting, handing out banners, whatever – the response is very positive. A lot of people want to talk to us, get the leaflets, sign up." He cites a series of debates staged on university campuses from London to Exeter to Bath, the last being held one week after last year's jubilee celebrations. "We did a vote at the beginning, asking people if they were pro, anti, or indifferent. We went from being in third place to having an overall majority by the end of the debate." Papers such as London's Evening Standard, which first reported this week's poll, emphasise the "halo effect" of last year's jubilee, when the percentage of those wanting to keep the monarchy rose to high of 80%; Smith says that the picture, from his point of view, is rather different: "On 16 November 2010, when William's wedding was announced, right on that day we had a spike of people phoning up. Between that announcement and the jubilee we went from having 9,000 to 30,000 supporters. And there'll be another boost when the baby is born."

"I think the republican movement is better organised and higher-profile than it has been for a long time," says novelist and commentator Joan Smith. "Last year I spoke at a republican demonstration during the Queen's jubilee celebrations and so many people turned up that the security guards wouldn't let them through – there were hundreds of republicans milling about."

The biggest change, argues Graham Smith, is not numbers so much as the fact that "there is now a republican movement": Republic acts not simply asa rallying point for the republican-minded, but as an active campaigning body. Nye's presence at the public accounts committee hearing was the direct result of lobbying from Republic, which as far back as May 2007 was persuading Brian Iddon, MP for Bolton South East, to table an early day motion about the lack of transparency in the Duchy of Cornwall's accounts. When Visit Britain claimed, before the royal wedding, that the event would be good for tourism, Republic made a Freedom of Information request for documents which duly revealed that in fact royal weddings had no such precedent. "If we look at the marriage of Andrew and Sarah in July 1986," wrote Visit Britain's head of research and forecasting, "we find that across the year as a whole there were 4% fewer visitors to Britain than in 1985, but that in July [1986] there were 8% fewer than in July of 1985. While this and the results relating to 1981 are inconclusive, such as it is, the evidence points to royal weddings having a negative impact on inbound tourism."

"The previous generation of republicans let the side down by treating it as an academic issue," says Graham Smith. "We're deliberately trying to move away from that and make it a political issue that's campaigned on. There's never been an organised republican movement before. Our challenge is to keep on building this movement and bringing more people into it and get over all the old cliches that have been around, such as the fact that these events [such as the royal birth] are a bad time for republicans, which isn't true."

The Royal Family on the balcony after the Queen’s birthday parade last summer. Photograph: Leon Neal/AFP

The so-called older generation, while in broad and largely enthusiastic agreement with his aims, are, understandably, not especially impressed with being written off in this way. "I think debating the principles of the constitution, which is what republicans want to do, should not be set aside as merely academic and not political," says Quentin Skinner, political historian and a lifelong republican. "It is highly political to talk about the principles and nature of a democratic constitution."

It is not the case that there has never before been an organised republican movement. "It's important to remember that England has been a republic," says Skinner. "There was an act of parliament – they didn't just cut off the king's head, they abolished the institution of monarchy. In English law the period between 1649 and 1660 doesn't exist. When Charles II came to the throne he was treated as if he had succeeded in 1649 – thus 1649-1660 was called the interregnum. They wanted us all to forget that there had actually been a republic."

And that act of parliament specifically stated that monarchy was being abolished because "it was said to produce a slavish people". Surely that no longer applies, when the monarchy has been entirely stripped of its powers? "I don't believe that," says Skinner. "There's garden parties, and honours lists, all sorts of institutions that help to produce deference." (All those reporters and camera operators expiring from heat and boredom in front of the Lindo Wing of St Mary's hospital in Paddington could be said to be enacting that deference, waiting powerlessly for a crumb of news about a royal birth, the symbol par excellence of unearned privilege.)

Republicanism has come to mean opposition to the monarchy, but historically it has been a broad church that has described all sorts of constitutional arrangements. It has been seen as compatible with a monarchy properly disciplined by law, for instance; it has not always entailed democracy. For Algernon Sidney, eventually executed for treason by Charles II, it was only absolute monarchy, not monarchy per se, that was evil; James Harrington's The Commonwealth of Oceana (1656) argued that republicanism was intimately linked with the ownership of land; the book was initially censored under Cromwell, then published with a dedication to him.

Republicanism was often used to describe a language of dissent – aimed at arbitrary government, against political corruption or anyone who put their own interest before that of the public. Its emphasis was on civic virtue and, following Aristotle, often presented good citizenship as a condition of liberty. Or it could have a more Machiavellian bent – to secure one's own freedom and interests it was simply rational to play a part in public affairs. For centuries, aristocrats like Philip Sidney and his ilk cast themselves as the only true republicans, because they were the only ones with sufficient resources to dedicate themselves wholly to the public good – an idea that Prince Charles, with his myriad projects for the supposed betterment of his people (Poundbury, lobbying for homeopathy on the NHS and so forth), would probably find quite attractive.

The next serious threat to the crown, says Skinner, was in the 1870s. "After the death of Queen Victoria's consort, Albert, and her withdrawal from public life, distinct republican murmurs were heard, enough to worry the government. People began to say, 'If this is someone who plays no role in public life, why do we keep her?' The republicanism of 1870 was a not-unimportant political movement and they had to take note of that."

More than a century later, after the royal family's "annus horribilis", as the Queen famously described 1992, and the death of Diana, republicanism seemed to have another chance – but the monarchy has concertedly fought back. It has, says Skinner, who, unlike both Smiths, believes republicanism to be in retreat, "very good PR. Bringing forward the young people, replacing the old-timers, the royal birth, the show continues." It's "a kind of opiate of the people. It's like pop stars, isn't it? They're simply in the news because they're in the news." And, perhaps, in a time of deep cynicism and disappointment in so many aspects of public life – bankers, politicians, clergy – they are seen as the least noxious of a bad lot; simple entertainment, even.

Graham Smith cautions, vociferously, against falling for this narrative. "They've won if we think they're harmless. What they're trying to do with these big events is promote three key myths that need to be challenged" — and which are the chief reasons that 75%-80% figure stays so steady: that the monarchy unites the country, that it is good for tourism, that it has no power. There isn't the evidence to support their argument for tourism, he argues – look at that Visit Britain memo. Furthermore, it is vital to separate the heritage tourism industry, which is thriving, from the antics of Princes Harry, William, et al: "Buckingham palace would still be there without the monarchy."

The Queen's sovereign grant was increased by £5m this year, which Michael Mansfield describes as 'staggering'

"One of the things I thought staggering," says Michael Mansfield, QC, another republican, who acted for Mohamed al-Fayed in the inquest into the deaths of Dodi al-Fayed and Diana, Princess of Wales, "was the increase of the Queen's sovereign grant. She's getting £5m more than she got last year. That was the day after Osborne outlined cuts of £11.5bn. Now, I know she's got expenses – I dare say the refurbishment of Kensington Palace is necessary but why does the public have to foot the £600,000 bill, rather than the Queen?" And on the subject of money, a quick call to Clarence House confirms that, public accounts committee notwithstanding, there are no plans to change the Prince's tax arrangements.

And then, of course, there is the issue of influence and power. About a year ago, notes Mansfield, "the attorney general ruled that we are not allowed to see the letters that go between Charles and government ministers. Why not? We're entitled to know what a potential head of state is saying." The decision was challenged by the Guardian but upheld in the high court this month. Mansfield thinks the biggest problem lies in "the willingness of people to recognise the parlous state in which we exist now – economic frailty overseen by someone who is not remotely in touch with it. [The Queen] may not have any actual formal power, but she has a lot of influence. What goes on between her and the prime minister when they meet every week? I'm sure they don't just talk about the weather – she's an intelligent woman, she'll have opinions. It's a very British form of power – indirect, diffuse, nobody writes it down, but there it is, year after year, century after century. Democratic governance must be transparent and accountable." The trouble, argues Skinner, "is that the Queen is very popular. She takes her job seriously and does it well, and people respect her for that."

This respect does not necessarily extend to Charles, and whether or not he succeeds, suggests Tony Benn, might eventually be down not to any kind of (polite) revolution, but to another very old form of British power. "The present system is that when the queen dies there is a meeting of the privy council, a strange body made up of ministers and former minsters. I've been a member since 1964, and it's never once met as a whole body. The privy council's duty is to proclaim 'with one heart, mind and voice' that the heir is the successor." This is in effect, he says, a unanimity rule: "In theory, if one of the members objected, [the succession] would be illegal. I think it's a possibility that has to be considered. There are a number of republicans in the privy council – whether anyone would do it, or it would be accepted as valid, I don't know."