Entry is to the United Kingdom, which (for now, at least) is still a member of the European Union.
For delegates entering the United Kingdom at Manchester Airport or other destinations in England, there are no further passport or visa checks when travelling between England and Wales.
Please refer to the following UK Government website for visa requirements:
https://www.gov.uk/government/organisations/uk-visas-and-immigration
The Welsh Correspondence Chess Federation will provide any necessary supporting documentation; please ensure that you allow sufficient time for your visa application to be processed (expected processing times are shown on the above website).