In a glowing endorsement, Miss Paltrow writes: 'Using Rachel's technique, Apple was sleeping through the night in a six to seven-hour stretch by six weeks.
'She was a very happy and settled baby from the beginning. I believe this is because Rachel put us in a routine so that Apple always felt that there was a loving structure around her. She knew what was coming and could look forward to it with certainty.'
Miss Waddilove, who has also worked for Lord and Lady Mountbatten, is a strong believer in breast-feeding but also advocates the use of a bottle to take the pressure off the mother.
In addition, she believes that babies should be left to cry for ten to 20 minutes in order to learn how to get themselves off to sleep.
'Many parents think that you need to rock them off to sleep in your arms, and then lie them down, but actually I lay the baby down in the cot, having swaddled them first, so they feel very safe and secure.
'If he can't settle, go in but don't turn on the light, stroke his tummy and talk to him gently, but then leave. If he still carries on for another 15 minutes, repeat the process.'
But not everyone is impressed with Miss Waddilove's approach and many mothers in the U.S. have condemned her use of 'healthy discipline'.
One said: 'Her advice is terrible. I'm sad for all the little ones who will cry and cry from hunger or the need for comforting as their parents lie awake in the next room thinking, "But Nanny Rachel says feeding on demand makes mums a slave to their babies".'
Another says: 'I can't believe that hippydippy, yoga/vegan Gwyneth would let someone with such a backward approach to baby-rearing into her house.'