The original supplier must charge UK VAT, as they aren’t exporting the goods. The Czech company is also making a taxable supply of goods in the UK, for the same reasons.
If the Czech company is not already registered for VAT in the UK, they may need to be. If they are a “Non-Established Taxable Person” (as defined in section 9 of HMRC Notice 700/1: https://www.gov.uk/government/publications/vat-notice-7001-should-i-be-registered-for-vat/vat-notice-7001-should-i-be-registered-for-vat#non-established-taxable-persons-netps-basic-information), they will be required to register for VAT because of this transaction alone – otherwise the normal VAT registration threshold applies.