It “should be” free to make a SEPA transfer from that Barclays account, but it isn’t. The SEPA directive merely says that SEPA transfers to any SEPA country must not cost more than national transfers in Euros inside the country. As there is no national system for transferring Euros inside the UK, the banks can charge what they want for SEPA transfers. Santander UK charges £25 (ridiculous).
Now, it used to be the case that BACS had the possibility of sending Euros within the UK, but that facility was shut down not long after the SEPA system came into effect. So there is no competing “free” national transfer system for Euros, and I think CHAPS (if it can even cope with Euros) is not a free transfer system. Faster Payments is for Sterling only. So we’re stuck here in the UK with banks charging what they want for SEPA. Only competition from the likes of Revolut might bring a change to that, but with the UK heading out of the EU and the Single Market, my bet is that banks will start to charge even more. We might even lose SEPA as we could well be ejected from the Single Euro Payments Area. All bets are off currently.