From the glittering office towers clustered by the waterfront, to the spotless malls crowded with perfectly coiffed shoppers, it’s hard not to feel transported into the future when you arrive in Singapore – a hi-tech, consumer-oriented kind of future of designer heels stepping into driverless cars.

From its humble beginnings as a mosquito-ridden tropical port, Singapore has transformed itself into one of the world’s richest countries. The south-east Asian city-state also has some of the world’s lowest taxes; its corporate rate is 17%, with temporary rates as low as 5% for companies willing to set up a regional headquarters there.

Little wonder, then, that Singapore has become the sweetheart of a certain kind of Brexiter. “If we are to thrive, our post-Brexit model should exactly be Singapore, a tiny country devoid of natural resources but with a booming economy and an average life expectancy of 85,” wrote Conservative MP Owen Paterson in the Daily Telegraph this week. In this vision, what Britain needs is a little more east Asian laissez-faire: “low-tax, low-spend, low-regulation”, in Paterson’s words.

Having autonomy is not the same thing as having power

This is mostly based on a fanciful idea of the far east as a free-market nirvana that doesn’t chime with my experience of living and working there. Indeed, that illusion is quickly dispelled by some basic facts. More than 80% of Singapore’s population lives in subsidised, government-built housing, while the state pervades the economy – Singapore’s state investment fund Temasek is majority shareholder of big companies like Singapore Airlines and the telecoms operator Singtel.

Turning the UK into a North Atlantic Singapore would also require a radical transformation of the British economy. It is true that Singapore is a major financial centre, but its wealth is not based solely on banking. Manufacturing – from electronics to speciality chemicals – accounts for a fifth of Singapore’s GDP compared with a 10th in the UK. Besides, much of Singapore’s attraction to investors lies in the fact that it is a stable country, with sound governance, in a corrupt and autocratic region. Gambling with its global reputation on the basis of a referendum is not really Singapore’s style.

However, there might be a nugget of fact in the fantasy. Singapore does offer a couple of pointers to Britain’s post-EU future – even if they aren’t quite what Brexiters imagine.

Here’s one example. Everyone knows that you can’t buy chewing gum in Singapore; this is regularly cited as evidence of founding father Lee Kuan Yew’s fastidious control freakery. Fewer know that this restriction was relaxed a few years ago – allowing the sale of “therapeutic” gum – in a concession that helped seal a trade agreement with the US.

A second example: while Singapore has plenty of migrants, the country tightened restrictions on foreign labour after elections in 2011, in which the ruling party got its lowest-ever share of the popular vote. The bruising election result was partly blamed on public disquiet over migration; voters grumbled about overcrowding on public transport.

Singapore’s leaders are fond of comparing the country to a speedboat, smaller and more agile than the world’s super-tanker nations. So, there might be a model for Brexit here: a UK outside the EU would enjoy greater autonomy, whether in trade talks or immigration policy.

But there are two problems when it comes to adopting this model. The first is that Singapore’s freedom to decide does not automatically bring economic benefits. Curbs on foreign labour mean Singapore’s restaurants and retailers now face higher costs and squeezed profit margins. Last year, the country’s central bank acknowledged that maintaining economic growth in the face of labour shortages is “probably the biggest challenge facing us”.

And having autonomy is not the same thing as having power. Singapore’s leaders are conscious that they must tread warily when they deal with Asia’s titans – especially an increasingly assertive China.

One obvious way for a small nation to magnify its voice is to stand together with a regional bloc. But Singapore’s neighbours are divided between vassals of China and those countries with military ties to the US. These tensions have come to a head over the South China Sea, the strategic waterway through which much of the world’s oil passes.

Singapore regards international arbitration as the way to deal with the dispute – a position that annoys China. When Singapore maintained this stand, the city-state found itself the focus of mounting hostility from Beijing, culminating in the impounding of a batch of Singaporean armoured personnel carriers in Hong Kong last year.

There is a deep vein of pessimism running through Singapore’s collective psyche. This is regularly reinforced by the government, which drums the notion of national vulnerability and self-reliance into its people. Giant posters in Singapore schools remind children: “No one owes Singapore a living” and “We must ourselves defend Singapore”.

Some Brexiters may regard Singapore as a model for a British future, but there are few in Singapore who would be quite so optimistic about going it alone. They know that speedboats may be more agile than super-tankers, but they are more vulnerable on the open sea.

• Jeevan Vasagar worked in Singapore as the Financial Times’s correspondent between 2015 and 2017, and is a former education editor of the Guardian