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Visitors have alleged that the Mayfair establishment is charging increased prices to customers that they don't recognise.
Brian Richardson, 52, told the Daily Telegraph: "On Monday I paid £3.50 for a pint, now all of a sudden it's £3.90.
"I was shocked. I complained to staff. They have got two prices - regulars prices and non-regulars prices.
"There is no price list on the wall. I don't mind paying more but it is completely arbitrary. It is not the money, it is the price hike. It is outrageous."
Westminster Council is looking into the customer complaints.
A spokesperson for Trading Standards said: "Given the allegations made the council will be seeking to speak to the licensee."
Madonna and Guy Ritchie are believed to have a 20% stake in the pub.
