Now you've explained the background, it sounds to me as if the club would prefer you to do English songs because you have (as you say) an English accent and a substantially English background.
I'd guess that they already get plenty of Irish stuff and would welcome a bit of variety. Since they've heard you before, they now know what you'll do if they don't specify their preferences, and they evidently prefer you doing English material. That doesn't sound unreasonable to me.

I don't think you (or they) can make any assumptions about your "blood"; it's your musical experience and background that count. Of course quality matters too, but I don't see why the quality should be any different if you do English songs and tunes.

The club are presumably paying you, so they're entitled to say what they'd like to hear from you. If you can't or won't put together a good-quality English set, then just say so and forget it.


Marje