Kay Franklin had bowed to requests from her daughter Jenna, now 15, who said she needed the surgery to boost her self-confidence.
Jenna, and her parents, from Warsop Vale, near Mansfield, Nottinghamshire, had already been criticised by health experts for considering the operation
The Franklins run their own cosmetic surgery advisory service.
Dr Erian said breast augmentation could benefit a lot of people.
But he added: "I feel at 16 the breast hasn't matured enough. Also, there would be a lot of psychological implications.
"One has to wait and see what God gives us, when she breast feeds. Also changes happen when you take the pill also happens as the breast gets bigger.
"If it doesn't change at 18 or 19 then we can think about it."
Jenna's mother Kay, who has had two breast implant operations, said she did not want Jenna to have any "hang-ups" about the way she looked.
And she said if that meant her daughter having a breast enlargement operation then she would gladly pay the £3,250 fee.
Consultation
Mrs Franklin told the Daily Express: "There are so many young girls who are depressed or bothered about the way they look. If you can do something about it, that's great."
But, even before the surgeon spoke out, she said the operation would not go ahead if the surgeons decided Jenna was not physically ready.
Jenna, who highlighted Pamela Anderson, Melinda Messenger and Emma Noble, as celebrities who found success after breast implants, asked for the breast enlargement as a 16th birthday present - after thinking of having enlargements since the age of 12.
She decided last year she wants to increase her breast size from 34A, to a C or D cup size.
She said: "You've got to have breasts to be successful. Every other person you see on television has had implants.
"I just want to be happy with my body and I think having my breasts enlarged will give me more self-confidence."
She said she had grown up with plastic surgery and did not see any problem with it.
"My parents are not being irresponsible - it's not for anyone else to criticise the decision I have made."
Criticisms
Health specialists and politicians have condemned the family's plan, saying the operation could leave Jenna psychologically damaged.
They said cosmetic surgery was a dangerous way to resolve teenage anxieties.
Ruth Coppard, a child psychologist form Sheffield, warned Jenna could be storing up problems for the future if the operation goes ahead.
"Emotionally, she is at risk by making a decision now when she's a child that will have long term repercussions that she can't consider yet, she hasn't got the perspective."
Tory frontbencher Ann Widdecombe said: "I think it's shameful that this girl is being encouraged to put looks and image above the more important things in life at such a young age."
The British Association of Plastic Surgeons has also said the operation should not be carried out at such at such a young age.