Both EU and UK will collect VAT on all B2C shipments from outside of their territories. The Low Value Consignment (LVC) thresholds, 150€ and 135£ respectively, allow for collection of VAT at the time of sale and require a registration. For EU it is IOSS and UK VAT registration. There are no duties for LVCs.
The UK registration is surprisingly simple procedure and you can do it yourself. Not sure if South-Korean companies require a fiscal representative in UK, however. IOSS requires an intermediary for everyone. Both roles can be quite costly due to the liabilities they bring.
We at EAS Project are providing an automated, cost-efficient and comprehensive EU solution with Intermediary function. The same solution also handles the UK, but the VAT registration has to be done independently.