Stan, I didn't hear the Radio 3 programme, but I suspect they may have been referring to work visas for professional musicians. Those rules are set by individual countries and travelling musicians will need to check with them, although it appears that many are willing to allow visits for cultural purposes without a visa.

CITES is an international treaty governing cross-border movement of endangered species. The EU is a single entity for CITES purposes, so it applies to anything going in and out of the EU, but not to movement within it. Previously that included the UK, but now travel to the EU is "cross-border" and CITES may now be relevant if your instrument contains certain species.

Instruments are supposedly being made an exception, but finding where that is stated and what documentation may nevertheless be required is difficult. At present, obtaining a Musical Instrument Certificate seems to be the safest option, but the forms are far from easy to understand.