Critics said the announcement – to replicate a deal with six southern African nations – fell far short of boasts, before the referendum, of a new free trade area much larger than the EU.
They also pointed out that it came amid doubts about whether the UK will be able to retain deals the EU has struck recently with Canada and Japan – which are far bigger economies.
Last year, Britain exported £2.4bn worth of goods to the six African countries included in Ms May’s deal - just 0.7 per cent of the value of its exports to the EU and the rest of the world combined, which were worth £339bn.
The government has acknowledged the risk of a “loss of trade” after Brexit with such countries, admitting they could demand more favourable terms to agree a rollover with the UK.
Speaking in Cape Town, the prime minister announced an additional £4bn of UK investment in African economies, with the hope of further match investment from the private sector to come.
And she said: “That’s why I’m delighted that we will today confirm plans to carry over the European Union’s Economic Partnership Agreement with the Southern African Customs Union (Sacu) and Mozambique once the EU’s deal no longer applies to the UK.
“As a prime minister who believes both in free markets and in nations and businesses acting in line with well-established rules and principles of conduct, I want to demonstrate to young Africans that their brightest future lies in a free and thriving private sector.”
Of those countries, South Africa was Britain’s largest trade partner in 2017, buying £2.4bn worth of exports, followed by Namibia (£39m), Botswana (£24m) and Mozambique (£11m). Lesotho and Swaziland purchased less than a million pounds worth of exported goods from Britain each.
But Tom Brake, the Liberal Democrat Brexit spokesman, said: “Theresa May is clearly delusional.
“Simply replicating deals already struck by the EU proves the Tories are in such a mess that their aspirations reach no higher than the status quo.”
And Gareth Thomas, a Labour supporter of the People’s Vote campaign for a fresh Brexit referendum, said: “Two years ago, Brexiters were promising a new free-trade area ‘10 times’ the size of the EU.
“Now they’re reduced to celebrating an agreement to roll over a fraction of the existing trade deals that we already benefit from as EU members.”
Mr Thomas said that Brexit “threatens to tear up” fresh EU deals “like the recent one with Japan”.
Lord Boateng, a Labour peer who is chair of the Africa Enterprise Challenge Fund, also warned the UK’s trade drive had “a lot of catching up to do” with the likes of China, France, India and Germany.
Britain hopes to roll over all of the EU’s current trade deals, with Chile, Israel, Egypt, Mexico, Russia, South Korea, Switzerland and Turkey among others.
However, the government was forced to drop a claim that the process was assured, while maintaining that “all partner countries have agreed to work with us to ensure continuity”.
Separating agricultural quotas is believed to be a key controversy, some countries rejecting a plan by the EU and the UK to divide the allocations between them, after the UK’s departure.
The Federation of Small Businesses (FSB) said strong trade ties with Africa will be crucial after Brexit, with 35 per cent of its exporting members sending their goods to Africa.
Mike Cherry, its national chairman, said: “Export vouchers should be made available to small businesses, as this can pave the way to new export deals.
“Our own figures have shown that members are increasingly looking at the emerging markets and it’s important that this continues in the coming years.”
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