Funnily enough, I had this conversation with my six year old nephew a few days ago. Well, he asked me “What if the Barbel all disappeared? Would you fish for carp or something else?”
I answered no to the carp, I fish for them a few times a year - usually they’re either too easy or too difficult (depending on the time of year), they’re never the right amount of ‘challenge’. Paraphrasing Mr Crowhurst too, sod targeting the big ones!
So in answer to his and the OPs question, I’d probably answer:
Tench - April - June
Barb... Damn it....

Catfish - July - August (never caught one)
Perch/Pike/Chub - September - March
Here’s the nephew with his first ever Barbel on a family holiday to the Wye a few days ago. Let’s hope both his question and this thread remain hypothetical, because he’s definitely ‘one of us’ in the making!