In an interview with Town & Country magazine, which has dedicated its spring issue to the Queen's 90th birthday, Dr Mugford revealed details of the lives of the royal pets behind closed doors.
"At feeding times, each dog had an individually designed menu, including an array of homeopathic and herbal remedies," said Dr Mugford, describing a visit to the Queen's inner circle.
"Their food was served by a butler in an eclectic collection of battered silver and porcelain dishes.
"As I watched, the Queen got the corgis to sit in a semi-circle around her, and then fed them one by one, in order of seniority. The others just sat and patiently waited their turn."
The dogs have previously been reported to be fed on a diet that included fillet steak, chicken breast and gravy, with scones crumbled up into their bowls for a treat.
Speaking of the Queen's love of animals, Dr Mugford continued: "The Queen has definite views about how dogs should be cared for: she doesn't tolerate unkindness, and I remember she took a very dim view of President Lyndon B Johnson picking his dogs up by their ears.
"When she's talking about her dogs or her horses you see a completely different side to her: she relaxes.
"Dogs are great levellers, and they're not influenced by social status, which must be a great relief to her. No wonder she enjoys being around them."
The Queen's devotion to corgis, which were introduced to the Royal family by George VI, dates back to her 18th birthday, when she received Susan, a Pembroke, for her 18th birthday.
She has gone on to own more than 30 of the dogs, all descended from Susan, which are often photographed accompanying her on and off duty.
She currently owns just two, Holly and Willow, with two other dorgis - a cross-breed of a corgi and a dachshund - named Candy and Vulcan.
It has previously been reported that the Queen will not introduce any new corgis to her royal household.
The spring edition of Town & Country, which goes on sale on Thursday, will include a portfolio of rarely seen photographs from her reign, as well as the recipe for Prince William's favourite chocolate cake.
The magazine is one of many publications to mark the Queen's 90th birthday this year.
A new book, published by the Bible Society, Hope, the churches' group, and the London Institute for Contemporary Christianity, also celebrates the long reign.
Writing in the foreword, the Queen said she was "very grateful" for the country's prayers and that she had
felt God's "faithfulness" throughout her reign.
"The extent and pace of change has been truly remarkable," she said, in The Servant Queen And The King She Serves. "We have witnessed triumphs and tragedies."
