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The Oriental Club in central London banned cellist Katherine Jenkinson from taking her 11-week old baby and a babysitter into her dressing room.
The musician, who was performing at the venue as part of the Aquinas Piano Trio, had to breastfeed baby Olivia in the car.
She told Classic FM: "My 11 week old solely breastfed baby was refused entry to the Oriental Club in London where I was performing a concert. I had to breast feed her in a car outside the club before and during the interval of the concert and my babysitter walked her around M&S during the first half.
"The private club refuses entry to children under the age of 12 due to their 'byelaws'. I'd already arranged a second babysitter to be at home with my 4 year old son as I'm fully aware that it is often inappropriate to take children to such events. Does this really apply to a breastfed 11 week old babe in arms?
"Our dressing rooms were two floors down with beds (prefect for looking after a baby). No sound could possibly have spilt to the concert or other events. I found the way they handled the whole situation very upsetting, insensitive and quite frankly rude. We were keen to perform the concert so the trio remained as professional as possible."
The Oriental Club was founded in 1824 for “Noblemen and gentlemen associated with the administration of our Eastern empire.” It is open to men and women and costs £1,000 a year to be a member.
The incident comes just days after Claridge's caused controversy by asking a mother to "cover-up" while breastfeeding. A group of mothers protested by breastfeeding outside the London hotel on 6 December. The hotel said that it "embraced" breasfeeding but asked mothers to be "discreet towards other guests".
The Oriental Club has been contacted for comment.