"I was so shocked and humiliated," Ms Burns said.
"I have three children and this is the first time I have been able to breastfeed properly. Women are under so much pressure to breastfeed and it is not always easy. I did not expect to be made to feel I have done something wrong."
A senior manager came over after seeing how upset she was, but reportedly refused to back down.
Ms Burns then attempted to use the napkin but her daughter was distressed, and management eventually relented - providing other customers did not complain.
"I felt so awkward. They said they were very sorry and wanted to see me back there, but I was so appalled by my treatment. I was not out there with my boobs out. I was so discreet one of the waiters did not even realise I was breastfeeding."
Ms Burns said she wanted to walk out but the day had been organised months in advance by her mother, who was visiting from the Midlands.
A spokesperson for Claridge's said it could not comment on individual guests, but did say: "Of course we allow women to breastfeed - we just ask them to be discreet".
The spokesperson repeated this statement when asked if it was policy to ask women to cover themselves while breastfeeding their children.
- Independent