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Prospective parents are being offered in-vitro fertilisation (IVF) and a type of embryo screening called Pre-Implantation Genetic Diagnosis (PGD) which is outlawed in Britain except for women at high risk of having a baby with a genetic condition linked to gender.
The BBC said representatives of a fertility clinic in Turkey came to London to offer gender selection because of high demand from UK couples.
It filmed representatives of the Jinemed Center offering the procedure, which is also illegal in Turkey, at its Istanbul clinic.
The Turkish government, which is carrying out the inquiry into the Jinemed Center, has warned patients not to travel there for the treatment.
The BBC said the clinic offered to implant three embryos. Professor Peter Braude of King's College London, who advocates implanting only one embryo in women going for fertility treatment, said: "Putting three embryos back in a young woman is really bad practice because of the high risk of multiple pregnancy.
"So even if you went abroad for treatment and had your IVF treatment you're bringing those twins back for care in this...