What could be lovelier? A new park on the river Thames, south-facing to catch the sun, which like something in a fairytale would also float. Here people could bask and stroll, close to the lapping water, or splash in a swimming pool. It would be ready for the blessed summer of 2012, enriched not only by the Olympics, but also by the celebrations of Queen Elizabeth II's 60-year rule. It would make a perfect viewing point for joyous throngs to watch the 1,000-boat river pageant that is planned for the Queen's Jubilee. It would be like those Venetian paintings of aquatic festivals in La Serenissima, brought to life in the here and now.

The park, invented and designed by the architects Gensler, would run from the Millennium bridge and St Paul's Cathedral to close to the Tower of London and Tower bridge, linking some of London's prime tourist spots. It would serve the City of London, an area short of open space. It would be there for five years, after which it could be taken away if people didn't like it. It would also cost the public nothing. The Singaporean asset-management company Venus will pay the entire £50m cost, and has already put £5m into developing the idea, including building a 35-metre model of a 35km stretch of the Thames, to test the park's hydrographic effects. "We either do it beautifully," says John Naylor of Venus, "or we don't do it at all", to which end Venus doubled the budget that Gensler asked it for.

Boris Johnson is enthused. After an impromptu Sunday morning meeting with Gensler and Venus, he declared: "The sheer beauty and design brilliance of this structure will provide yet another amazing and unique attraction for the capital." Daniel Moylan, of Transport for London, has said of it that "improved connectivity, gracefully designed, can bring pleasure and joy to an area once written off". The outgoing Lord Mayor of London, Michael Bear, was said to favour the scheme, as a legacy of his mayoral year, although the Corporation of London would not confirm this. Gensler and Venus claim "overwhelming backing from Londoners" although this turns out to be based on an unscientific poll of whoever turned up to two exhibitions of the proposals.

But there is, as the economists have taught us, no free lunch. Venus is not putting up all this money out of the pure goodness of its heart nor, entirely, to raise its "brand awareness" in London, as John Naylor puts it, although that is a factor. It is "looking to create a platform for inward investment" and intends to make money renting out pavilions in the park for corporate exhibitions and events, at a handsome rate. It also thinks it can sell space to TV companies, especially during the Olympics, using Tower bridge as a backdrop. It is almost certainly right. This means that the park is not a "public space", as Gensler calls it, but a private space into which the public are allowed to come, subject to certain limitations.

In this it is the latest example of a widespread type of the 21st century, the pseudo-public space, in which the City of London and its satellites are world leaders. The Broadgate development of the 1980s was a pioneer, followed by Canary Wharf, Paternoster Square next to St Paul's, and the More London development where City Hall, the headquarters of the Mayor of London, stands. In each the shapes and attributes of town squares are imitated – an oblong or round shape, outdoor art, cafe tables, fountains – and sometimes real public assets are created, but ultimate control is in the hands of private landowners. As Anna Minton pointed out in her book Ground Control, they control security, access, and rules of entry. Activities and people deemed undesirable, such as photography with a tripod, public displays of affection, picnics, or chaining up a bicycle, are banned. Or public protest, and you don't have to wish to protest yourself to sense the oppressive feeling that things are prohibited. The most extreme example is the "public park" promised for the top of the forthcoming "Walkie Talkie" tower in the City. By no stretch of the imagination is a roofed-over room in a private office tower, reached via security-controlled lifts and lobbies, "public".

These places had their bluff called by the Occupy movement. Anxious to keep out the tented rebels, Broadgate and Canary Wharf reached for the injunctions that asserted their rights as private landowners. Paternoster Square put up barriers, manned by both police and private security, that jarred with its architectural look of traditional civic values: arcades, monuments, streets, stone and brick, a classical style.

It also put up a sign that said: "Paternoster Square is private land. Any licence to the public to enter or cross this land is revoked forthwith. There is no implied or express permission to enter the premises or any part. Any such entry will constitute a trespass." Which is strange, as almost every architectural statement, planning application, and press release, in the protracted redevelopment of Paternoster Square, described this "private land" as "public space".

These spaces (what shall we call them – privlic, publate – let's say publoid) don't always have to be bad things. Cities are made of places with degrees of publicness, including museums, restaurants, theatres, shops, malls and transport systems. Canary Wharf and Broadgate were both built on sites that formerly had limited public access – docks in one case, a railway station and its tracks in the other – and offer more to the public than they did before. The sky garden of the Walkie Talkie might turn out to be a fun place to go. (And, if they try to pressure you into buying expensive drinks at its bars, you will be able to whip out the planning consent that says it is a public space.)

But one issue is the honest use of language. If a space is private, it should not be called public, and planners should send back any application that makes this false claim. This matters because, if we are kidded into thinking that there is a civic realm that is not actually there, we will suddenly find that there is less space than we had thought for such essential public actions as protest. This is what the Occupy movement found when it looked for a location to make its point in the City of London. It turned out that the Square Mile is cunningly designed so as to have almost nowhere for such groups to gather, so the protesters ended up by the skirts of St Paul's. Oddly, the Occupy movement looks like the sort of colourful cultural event that local authorities and even businesses pay good money to subsidise, so as to jolly up their town centres: it is only when they are trying to say something that they officially become a problem.

The bigger issue comes when publoid places occupy areas that were formerly genuinely public. Then they are not conditional gifts, as at Broadgate, but appropriation. The banks of the Thames are largely public – you can walk there unrestricted, and advertising is kept from the waterfront. The view of the water is public property, and one of the great free pleasures of London.

It may, conceivably, be possible to cut deals with the private sector if they are genuinely beneficial, but only when it is completely clear that the public qualities of a place are not being compromised. This is very far from the case with Gensler's designs for the London River Park, in which budget and architectural ambition are lavished on the silvery pods which will house the money-making stuff, while the offer to the public is ordinary-looking, standard-issue publoid design: some trees and benches of reasonably good quality, a stainless steel balustrade, a nondescript deck surface, the promise of some information panels explaining the history of the surroundings.

An obvious comparison, made by Gensler, is with the High Line in New York, the phenomenally successful park made out of an old railway viaduct, which like the River Park is long and thin. But a big part of the High Line's success is its planting and landscaping, which is intelligent, imaginative and well considered, in the way it converts industrial relics into a place of urban pleasure. There is no sign of this level of thought in the Gensler design, even though they have submitted a detailed planning application to the Corporation of London. Nor is there the playfulness of Paris Plage, the annual conversion of the banks of the Seine into a beach, or the floating swimming pool that was installed in Copenhagen. Gensler is a global practice, with more than 3,000 staff, but there is limited evidence in its portfolio that it has the touch and finesse to pull off a project like this.

Instead the park offers a marginal upgrade on the existing riverside walkway. It would be wider, and with a more intimate relationship to the water. On the other hand you would lose the sense of unrestricted wandering and gathering that is currently there. You would be all too aware of the selling going on in the pavilions. You would know you were in a managed and controlled space, with uniformed wardens. This, says John Naylor, would be like Disney World, to the extent that "you know you're protected; you know that you won't be attacked or bothered by vagrants and sellers" (except, of course, for the approved corporate sellers in the pavilions). Is the City of London such a crime zone, financial misdemeanours apart, that people need such protection?

Essentially the London River Park is a gigantic hospitality suite with a fairly nice walkway threaded through it. Meanwhile the design of its silver pods is offensively indifferent to the dignified buildings, such as Old Billingsgate Market, on which they intrude, and actually do not seem well suited to the events that might go on inside them. The only purpose of their look seems to be self-promotion. It is, for good measure, likely that the piles that hold the park in place will, at low tide, be unpleasantly conspicuous.

As it happens, the park idea is not meeting with unanimous approval, despite the support of the mayor. Cabe, the Commission for Architecture and the Built Environment, said that "we are not convinced by the description of the project as a 'park'" or that it is "appropriate to the character of the river". They find the design of the pavilions "unimaginative". English Heritage noted that "temporary" constructions like this have a way of becoming permanent. They were "not convinced that the design was worthy of such a sensitive site", and thought that the view towards the dome of St Paul's "would be distracted by the blades of silver", which are "flashy and corporate". The City of London School for boys, which is on this stretch of embankment, is none to happy that these large objects will block its view of the river.

When I meet Gensler and Venus, they assure me that discussions are going well with the Port of London Authority, which manages the river and is notoriously picky about intrusions on it. They also say that the planners of the Diamond Jubilee are very interested in their ideas. The next day, however, it is announced that the PLA has "serious concerns regarding the application scheme's impact on navigational safety", and the Corporation of London is delaying making a decision about the planning application. I also see a letter from the Diamond Jubilee organisers, saying that the park would "have a significant negative impact on the river pageant". It would for example make the tide run faster, with the result that rowed boats would be unable to take part, which would reduce the planned 1,000 boats by a third. Gensler and Venus have now given up on trying to be ready for the Jubilee in June, even though their extraordinarily ambitious timetable – to have everything ready for the Olympics – is still in place.

Buried deep within the London River Park is a good idea. If it were truly an aquatic High Line, it could be wonderful. It might work better if it were funded differently, let's say by a levy on all City businesses, such that it were no longer a promotional and profit opportunity for just one. If there were a longer timescale than the current insane rush to summer 2012, its design and detail could get the attention it deserves. It would also help if Gensler graciously stepped back from the detailed design, having been thanked and rewarded for having the idea, and pushing it thus far with energy and chutzpah, in favour of practices with the ability to think and work like those of the High Line.

If all these ifs were sorted out, the lovely floating park might just happen, subject to the satisfaction of the PLA. But there are an awful lot of ifs, and not much sign of the will to address them. If they are not addressed, the London River Park is simply an Occupy London event carried out by big business, rather than harmless folk in woolly hats and funny masks. The corporation's planners, when they finally get to consider it, should just say no.