All air and sea ports have been put on alert for missing 14-year-old girl and 35-year-old John Bush.
Police say sightings suggest they are heading south from Yorkshire and that any move to leave the country would be "very foolish".
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The boy is in a stable condition, his family has said.
The new scheme aims to speed up the permission process and allow applicants to apply from overseas and work in Ireland.
Since January 2010 there have been 35 collisions on the Thames involving older boats.