While I am unsure whether there is actually an economic benefit in having both a Sterling and Dollar card - apart from earning miles per dollar, you always have the option of applying for a dollar demoninated International Currency Card, which like the euro card, is actually issued in the UK.

This option would certainly make it easier if using your UK salary to justify - the issue will be if they want to give you two cards. I suppose one option - if it comes to that, is offer to have a lower notional spending limit on both charge cards.

Hope this is helpful.