Surgeons hope to replicate the success of the world's first-ever effective womb transplant, conducted on a 36-year-old woman in Sweden who gave birth last year.
More than 100 women have been approved as potential recipients ahead of the trial which is set to start in the first half of next year, after ethical approval was granted by the Imperial College London.
The procedure has previously also been attempted in Saudi Arabia and Turkey but in both cases did not lead to live births.
"There's an innate desire for many women to carry their own baby and this procedure has, potentially, the capacity to satisfy that innate desire," Smith told BBC radio.
More From This Section
Around one in 5,000 women is born without a womb, while others lose the organ as a result of cancer.
Smith said it was "heartrending" to meet those women affected.
Ten women will be selected for the trial subject to certain criteria being met. They must be aged 38 or under, have a long-term partner and be a healthy weight.
In a six-hour operation participants will receive a womb from a donor who is classed as brain dead but whose heart is still beating.