There are plenty of cards in the UK that do not have a foreign transaction charge on purchases (nationwide, lloyds avios, for example).
It got to a point I had to open local bank accounts and do wire transfers from my UK bank account to local bank accounts and use the local debit card. I just couldn't get my TSB/Lloyds card to work anywhere except high end western shops like Apple Store.
Was your experience all within the inner city?
For sure many coffee shops and convenience stores accept card, but I definitely find myself having to pay cash quite often (just for instance, the laksa place on Hunter street).