I got the same question some time ago while shopping (with my US-based card) at Harrods. So, on multiple purchases on the same day, I did some in GBP and some in USD.
When the charges posted on my stmt, I calculated that their conversion rate to USD was to the merchant's benefit. There's no rule that requires the merchant to use the "best" currency conversion rate. So, if asked, I always transact in the local currency.