Exchange rates & UK retail chains in Ireland

Just wondering with regard to the UK retail chains operating in Ireland who indulge in the practice of dual price labelling on their products (Stg and Euro), as a consumer, if paying by Debit/Credit card (Or even with Stg cash) can one insist that you are charged the listed Stg price instead of the Euro price?
With the constant strengthening of the Euro against Stg there is a considerable variation in the ratio that isn't reflected in the price labelling and certainly isn't being passed onto the Irish consumer.

I don't know the legal position, but I would suspect that a shop would be entitled to charge you the Euro price and refuse to charge you the price that's charged in Britain.

A shop in Ireland may well have different staff costs, different rent costs, different insurance costs etc., compared to its British counterpart so there may be factors that add to the Irish sale price outside of just the currency conversion.