Dr Fishel says there is extensive consultation
Fertility authorities may have another application for embryo selection within three months, the director of the Centre of Assisted Reproduction said.
Dr Simon Fishel, based at Nottingham's Park Hospital, said he had received three recent inquiries from overseas about the procedure.
Raj and Shahana Hashmi's three-year-old son Zain has beta thalassaemia major which creates potentially fatal levels of iron in his blood.
His condition can be cured only by a bone marrow transplant from a perfect genetic match with no suitable donor yet found.
Fundamental make-up
Embryo selection will allow cells from the designer baby's umbilical cord to be used for a transplant to save Zain's life.
The couple, from Moortown in Leeds, justified their decision by saying that they were not picking physical features like the sex or eye colour, but the fundamental genetic make-up.
Dr Fishel told the Press Association news agency: "There are six other couples who have expressed an interest because they cannot get a match from the donor bank."
The couples are at the beginning of the process with no guarantee they will all proceed.
He said: "The process the Hashmis went through included extensive medical and scientific consultation."
The couples hoping to follow the Hashmis would also go through that consultation in addition to counselling on the implication of their decisions.
He said all the couples had children with life-threatening conditions.
Blood transfusion
Mrs Hashmi told the Mail on Sunday newspaper: "This baby is going to be a special gift from nature, not a designer baby.
"We are not destroying anything. We are not hurting anybody."
Zain is currently given injections every day and a blood transfusion every three to four weeks to keep him alive.
The treatment causes side-effects like night blindness, aching muscles and limbs, swollen legs, sickness, diarrhoea, rashes and tiredness and his parents are desperate to relieve him from the pain.
Critics are worried the HFEA ruling will pave the way for more designer babies and couples being able to select physical features .
Living nightmare
But Mrs Hashmi, 37, said that Zain too had a right to life and that she had a duty, as his mother, to help relieve his pain.
She said: "It has been a living nightmare for him.
"And when he gets a little bit older, he will know he is going to die.
"How is he going to feel if he knows something could have been done to save his life?"
The other embryos created as part of the selection will not be destroyed but will be frozen.