Despite the unscheduled stop the royal couple transferred to cars and continued on to the market town of Hay-on-Wye by road.
They finally arrived close to three hours late but emerged looking relaxed and smiling to be greeted by a crowd of several hundred well-wishers.
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Michael Fallon has received reassurances from his US counterpart that security ties with Britain will "endure" following a vote for Brexit.
On Friday, police said it appeared the girl had shot herself in the face with the weapon.
The showers will be slow-moving, heavy and thundery at times, particularly in central and eastern areas.