Members of the United States Congress are on a fact-finding trip to find out more about stem cell science in the UK.
Mr Bush met children who were adopted as frozen embryos
The bipartisan group says it fears the US will fall behind the rest of the world in research into this area.
In May, the US House of Representatives voted to increase government funding for embryonic stem cell research.
But President George W Bush, who has strong objections to the work, has vowed to veto the bill if it is passed the Senate.
No date has been set for the Senate vote.
The debate over embryonic stem cell research provokes strong opinion, dividing those who say the research is vital for medical progress, and those who say it destroys human life.
Researchers believe stem cells - which can transform themselves into many other tissue types - hold the key to finding cures for many diseases, including Parkinson's and diabetes.
But there are religious and ideological objections to their use from campaigners who say the five-day-old embryos from which the cells are taken represent the earliest stage of life.
'Crossing the line'
Republican Congressman Mike Castle was part of the group who came to the UK which met scientific researchers and MPs.
STEM CELL MILESTONES
1960s: Research begins on stem cells taken from adult tissue
1968: Adult stem cells used to treat immune deficient patient
1998: US scientists grow stem cells from human embryos and germ cells, establishing cell lines still in use today
2001: Embryonic stem cell turned into a blood cell
They also met representatives from the Human Fertilisation and Embryology Authority, which regulates any research involving embryos and which does not have an equivalent in the US.
He told the BBC: "I'm concerned the US has fallen behind countries such as the UK and Asian countries because of the restrictions imposed on embryonic stem cell research.
"We have a very limited number of lines at the moment, about 22, for our researchers to work on which is insufficient to get a body of work to the level it needs to be."
Mr Castle said they had also met a US scientist who had come to the UK to work on stem cell research.
"It's a brain drain; an economic drain as well."
However, he said it was unlikely his bill would be introduced, because of President Bush's opposition.
But he said he hoped it would encourage informed discussions about the issue.
Many Catholics and social conservatives in the US oppose the destruction of embryos.
President Bush said in May: "This bill would take us across a critical ethical line by creating new incentives for the ongoing destruction of emerging human life."
"Crossing this line would be a great mistake."
There is no law against private stem cell research, which is moving ahead in states like California.