Nobody knows about the UK’s post-Brexit study-abroad scheme because the Government does not promote it well enough, the Foreign Secretary has suggested.

Britain turned down an offer to continue participating in the European Union’s Erasmus student exchange scheme after Brexit and has instead replaced it with the Turing scheme.

Lord David Cameron insisted the Turing programme is “more generous” than Erasmus in many ways but that fewer people are aware of it.

He revealed that one of his own children, who is currently deciding where to go to university, had “never heard” of the scheme.

At a Q&A with students at Astana University in Kazakhstan during his five-day diplomatic blitz in Central Asia, the Foreign Secretary said: “I think (we) do not promote Turing well enough.

“I think everyone knew about Erasmus, nobody knows about Turing. And I think what the Foreign Office has got to do, and also the education department and the other departments, is promote it.

“I want every child in school… I’ve got an 18-year-old who is currently deciding where to go. He’d never heard of Turing. He’d heard about Erasmus and the fact it wasn’t available anymore.

“I think we’ve got to advertise it more because, in fact, it is in many ways a more generous scheme because it enables you to go to universities around the world.”

Erasmus covers placements across the bloc and some countries outside that pay to be a part of the programme, while the Turing scheme announced by Boris Johnson provides placements across the world.

But analysis of the first year of the new programme found a number of problems, including students forced to drop out because places were confirmed too late while others failed to receive funding.

The report by IFF Research suggested four out of five universities (79%) had difficulties with the application process.

Lord Cameron said he believed Turing was the “right approach” because of its wider scope as well as greater access for students from less advantaged backgrounds.

“If we went back to that, and of course, it’s an option – it’s always an option, you could always opt back into the Erasmus scheme – but being rational about it for a moment, given that many more Europeans were coming to British universities than Brits were going to European universities, actually opting back into Erasmus would cost us a lot more money without more British students benefiting,” he added.

Lord Cameron resigned as prime minister the morning after millions of Britons voted to leave the EU, having led the campaign to remain in the bloc.

The former Tory leader made headlines earlier this week when he suggested he would “love” the UK to have a migrant returns deal with France but “it’s not possible because of the situation we’re in”.

The comments were widely seen as at odds with the Government line that an agreement with an EU country is not possible because the bloc would insist Britain take a quota of migrants as part of the arrangement, though Lord Cameron later denied he meant Brexit was to blame for the lack of a cross-Channel deal.

He said that the Dublin Regulation – the EU rules which allowed member states to transfer asylum seekers to other countries in the bloc – “no longer exists whether you’re in the EU or out of the EU,” and that the Government has looked at “innovative solutions” like its Rwanda deportation scheme instead.

Lord Cameron made the remarks as he travels across Tajikistan, Kyrgistan, Uzbekistan, Turkmenistan, Kazakhstan and Mongolia in a diplomatic bid to bolster trade and security relations with Central Asia.

Becoming the first foreign secretary to have visited Tajikistan, Kyrgyzstan and Turkmenistan, the minister said he has had “constructive talks” with leaders from across the region.

Following a bilateral meeting with his Kazakh counterpart Murat Nurtleu, he said his message to Central Asia was that Britain wants “to be here so you have a choice” to partner with Western countries as well as Russia and China, which have vied for influence in the region.

The trip has seen the Foreign Secretary help prepare a dish of traditional Uzbek plov and step inside a Turkmen yurt as he seeks to forge closer cultural and business ties with Central Asia.

Among the announcements he has made is a new scheme designed to promote the English language in Central Asia, as well as a doubling in the amount of its funding for Chevening scholarships, which allow people from abroad to study in Britain.

He flew to Mongolia on Thursday, where he met the country’s foreign affairs minister Battsetseg Batmunkh at the ministry of foreign affairs.

In a room packed with local media, Lord Cameron told her that the UK wants to be “one of your best neighbours”.

“We admire the journey you’ve been on as a country,” he said. “We’re grateful to celebrate your democracy and your success.”