With Theresa May’s Brexit deal in tatters after Tuesday’s vote, it may still be possible that Britain will leave the EU without a deal. However, for those who would like to remain EU citizens, but don’t have the necessary relatives to enable them to apply for a passport, there is another way: golden visa schemes.

Although these schemes, which offer residency or citizenship in return for buying property or investing in a country, are open only to non-EU citizens, worried Britons have been inquiring since the country took the decision to leave the EU in 2016.

Paul Williams, the chief executive of La Vida, a specialist in golden visas, says: "Inquiries started the day after the referendum and haven’t stopped. The schemes are only open to non-EU members though, so our advice is wait to see what deal is struck. If people invest in property now, we don’t know whether they will retrospectively be able to apply for residency if we leave the EU, so it is a risky strategy."

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Britain is not due to leave the EU until December 31, 2020. Until then British people remain EU citizens and so cannot apply for citizenship or residency programmes unless they involve obtaining dual citizenship.

Williams adds: "If people are really worried, one option is to invest in property in Cyprus, where you will get a Cypriot passport and dual citizenship, so you will retain EU citizenship when the UK comes out. Cyprus is the only one to offer citizenship on investment in property."

Here is a rundown of the schemes and what they offer:

The villa in Paphos has a garden with cypress and olive trees

Cyprus You can have EU citizenship within six months if you invest €2 million (£1.8 million) in a residential or commercial property on the island. This is the most rapid citizenship on offer in the EU and gives buyers a Cypriot passport, enabling dual nationality for British buyers.

You can buy the property (or properties) as an individual or through a company and rent it out. After three years the investment can be reduced to €500,000 and you will retain your citizenship. You don’t need to live in the country to acquire citizenship.

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Georgina Reilly, the head of international sales at Select Resorts Properties, says: "The type of buyer and property on offer has changed because of the citizenship programme in Cyprus. You used to be able to buy less expensive properties, and the British had quite a presence ten years ago, but with the government programme offering permanent residency to successful applicants spending more than £267,000, and full citizenship to those spending £1.8 million, international interest has increased substantially from Chinese, Russian, Asian and Middle Eastern buyers.

"This has led to an influx of luxury apartment blocks, mostly located in Limassol, along with high-spec villas with magnificent sea views changing the face of the Cypriot property market."

Portugal In return for property investment of between €350,000 (for properties needing renovation) and €500,000, a family can gain a two-year renewable residency permit. After five years they can apply for permanent residency, and after six years, citizenship.

Again the property (or properties) can be residential or commercial and can be rented out for income. There is no need to live in Portugal, although you do need to visit for two weeks every two years. Portugal doesn’t charge taxes on income for the first ten years of residency.

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Lisbon is one of the most popular areas for international buyers looking to invest. Paul Tostevin, an associate director at Savills, says: "Lisbon’s mainstream residential prices for the metropolitan area, at €1,400 a square metre, are 39 per cent of Madrid’s (€3,600 a square metre) and just 15 per cent of London’s (€9,300 a square metre). As economic and investment conditions have improved, residential prices have risen. Prime prices in Lisbon, which are driven by international buyers, have almost doubled since 2016."

Alex Koch de Gooreynd, a partner at Knight Frank, says: "The government has awarded more than 4,600 visas with new buyers coming in from Asia, Africa, South America and northern Europe. The second programme of note is the non-habitual resident regime, which is attracting individuals in receipt of pension income into a tax-free jurisdiction, for those who can benefit from the double tax treaty."

On the Costa Blanca, Spain, this three-bedroom villa is on sale for €545,000 through La Vida and makes buyers eligible for Spain’s golden visa scheme

Spain Spain also has a residency programme open to those who invest €500,000 in property. The visa can be renewed every two years and after five years you can apply for permanent residency. However, the permanent residency and citizenship, which you can apply for after ten years, require you to live full-time in Spain.

Jesús Fernández Salido, the chief executive of Mi Move Spain, a Spanish property portal, says in the year following the referendum in 2016 the British share of overall purchases in Spain went from more than 20 per cent to less than 15 per cent. He says the effect of Brexit diminished in 2018, and during the first quarter of last year Britons accounted for 14.3 per cent of all foreign sales. "The Brexit effect has already been accounted for in Spain, so the market is expected to remain stable in the coming months," Fernández Salido says. "Aside from the immediate impact of currency devaluation, much of the Brexit effect is related to the anxiety of not knowing what its impact on future daily life in Spain might be.

In Malaga, this five-bedroom villa is €1.9 million with Chestertons. Buyers are eligible for Spain’s residency programme

"Those who are buying have done their homework and realised that even the worst-case scenario of a hard Brexit will not likely have a drastic effect on an expat’s life. After all, Britons were already buying property in Spain before it joined the EU in 1986."

Greece The Greek golden visa programme grants those who spend €250,000 on a property five-year residency. This is the lowest-cost residency programme in Europe, despite taxes and fees of about €50,000 on a €250,000 purchase. You don’t need to live in the country to qualify, but if you want to apply for citizenship you will need to move there.

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Marcus Gondolo-Gordon, the founder of Incognito Property, an estate agency, says: "Buyers have seen the Greek economy being punished for many years, with property prices falling. These prices stabilised in late 2017, sat steady in 2018 and, in part thanks to an exponential rise in tourism last year, will see positive growth in the coming years, as we have seen in Portugal and Ireland recently.

"Along with the golden visa programme for overseas buyers, rental guarantee schemes are also a good way of securing a property that promises about 5 per cent return by handling the rentals on behalf of the owner for a fixed period," he says.

Other options Ireland and Malta have visa schemes that are more focused on general investment than property. In Ireland you need to have a net worth of at least €2 million and invest €1 million in an approved investment fund in return for residency. Investors can gain a €50,000 reduction in the amount needed for investment if they have children who go to university in Ireland.

Under the Malta citizenship-through-investment scheme investors must make a minimum contribution of €650,000 to the government’s national development fund, invest €150,000 in government-approved financial schemes and own a home, worth at least €350,000, in Malta for a minimum of five years.