The ministers will also begin work on an improved trade deal as Britain looks to use its exit from the European Union to build stronger ties with faster-growing economies throughout Asia and the Pacific.
"This is our Indo-Pacific tilt in action – strengthening ties with one of the largest economies in the world," Trevelyan said in a statement.
Monday's meeting is a precursor to formal trade negotiations, which are expected to begin later this year, to improve an existing agreement which effectively keeps in place the terms Britain had as a member of the EU.
Ahead of that, the delegations in London will look to improve supply chain resilience in the face of global disruption caused by the COVID-19 pandemic which is driving up production costs and fuelling inflation - currently at its highest in nearly 30 years in Britain.
Details of the agreement were not published in advance.
Britain said it wanted to ensure critical goods kept flowing between the two countries, citing chips used in advanced manufacturing as an example. Britain's auto industry, like others around the world, has been held back by a global shortage of semiconductors.
World leaders last year sought ways to strengthen supply chains by improving transparency and diversifying sources of key products.
Trade between Britain and South Korea was worth 13.3 billion pounds ($18 billion) in the year to September 2021, the government said. Both countries are seeking to join a trans-Pacific trade pact.
Leaving the EU has given Britain the power to strike bilateral trade deals, and ministers see South Korea and its wealthy middle classes as an important potential market for premium British goods, from folding bikes to pottery and Scotch whisky.
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