Local restaurant/businesses charge fee for non-UK credit card - how common?

You could, of course, pay cash.

They shouldn't discriminate between UK and non UK cards unless they are being charged more by their processor. They can only charge the direct cost borne for the use of a given means of payment. This won't be allowed after January 2018.

I have encountered this surcharge at pubs and B&Bs in London where if you pay with the luxury of using a credit card another 2 to 4% will be added to the bill, sort of like paying a nickle or more extra here when paying with a credit card at a gas station.

This is not a unique situation. There are small merchants in America that do something similar charging a fee for charges below say $10.00

I have not seen that myself. What I have noticed the last couple of years is restaurants adding a service charge to the bill. Fairly small maybe 8%.

In three trips to London in the past 9 months, I did not encounter any surcharge specific to using a non-UK credit card.

I have encountered this surcharge at pubs and B&Bs in London where if you pay with the luxury of using a credit card another 2 to 4% will be added to the bill

Fred, that is a charge for using a credit card, any credit card, to cover the fact that the credit card company does not pay them 100% of the amount billed. Websites (airlines, online shopping etc.) sometimes charge a credit card fee, which you can avoid by paying with a debit card.
Also some places have a minimum amount for credit card purchase (£10 or £20).
I would be very dubious about there being a charge for using a non-UK credit card, how could they tell it was a non-UK card until they scanned it?

You do however have to watch out for the dreaded DCC, where, after scanning your card, the machine "offers" to charge you in your home currency.

Pay cash and be done with it. Buy pounds from your bank before you go. Use CC for major purchases - hotel, car rental, etc.. Pay cash for everything else.

I've never seen it for a non-UK credit card. I have seen a few Sam Smith's pubs charge a 3% charge for paying by card. I enjoy their beer, so I just pay cash there and I'll have no hesitation in using coins when I'm paying unless it is super busy.