In the USA, yes most folks pay around 3%, but it gets lower when the card is physically present, aka swiped.

Now the EU has limited the Interchange Fee paid by EU merchants by an order of magnitude:

>For card payments carried out by the cardholder in a shop ("Card Present Transactions"):

> 0.2% of the value of the transaction for debit cards;

> 0.3% of the value of the transaction for credit cards:

>For online payments ("Card Not Present Transactions"):

> 1.15% of the value of the transaction for debit cards;

> 1.50% of the value of the transaction for credit cards.

Source: http://europa.eu/rapid/press-release_IP-18-6655_en.htm

And yet there are cards that offer 1 or 2% cashback in the UK - are these simply funded by the banks as a way to tempt users to sign up?

Most people miss the point that for a rewards card to pay you. You have to pay off the balance every month. And missing that by even a single month at 10%-21% interest that you get charged. You are more then likely to loose money even with the rewards.

if they're banking on a large percentage being online transactions, then the 1% could be covered or exceeded. Additionally, if they even break even on `transaction fees - cash back` then they make money on interest whenever someone can't/doesn't pay in full every month