Many Shia Muslims were banned from visiting the shrines under Saddam Hussein's regime and at one time Karbala was "razed to the ground", Mr Khoei said.
He added there were still dangers from different groups, including ones who believed visiting shrines was sinful.
He pointed out the Britons who died had been attacked in Baghdad, whereas in the south the majority of people were Shia and the region was considered "relatively safe" for them.
He said Shia Muslims would learn the history and importance of saints and imams as they grew up, so visiting the sites would be very significant.
"It is similar to a Catholic visiting Lourdes or a Christian visiting Bethlehem."