The move has been described as "historic", and the regulator will make its decision next month.
Doctors want to make babies from three people to prevent diseases that starve the body of energy, leading to brain damage, muscle wasting and heart failure.
However, fresh evidence suggests it will fail in one in eight pregnancies.
Three-person IVF replaces the defective power packs in the mother's egg - called mitochondria - with healthy ones from a donor woman.
A three-person baby has most of its genetic inheritance from its parents, but also a tiny amount from the donor woman.
Parliament has already legalised the controversial procedure, and a baby has been born from the technique in Mexico.
However, there have been calls for extra checks on the science before it goes ahead in the UK.
Prof Robin Lovell-Badge, one of the researchers who reviewed the evidence, said the moment had come.
"We're not going to learn much more now unless you try it out for real basically - it's at that stage," he said.
"There's no reason why it shouldn't go ahead now, but do it cautiously on selected patients where the risk of having a badly affected child is very high.