Oxfam says that some 670,000 people have left Syria since the crisis began in March 2011 but numbers have risen recently. In Jordan alone, the number of people crossing daily trebled in the past week.
The cold weather has seen an increase in the number of those suffering respiratory infections and pneumonia, according to the aid agency, which is distributing mattresses, blankets, heaters and gas oil to help new arrivals.
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Passengers, including a pregnant woman, say they have been stranded since 4pm yesterday.
The boxer said it was the "least he could do" and even donated the £30,000 shorts he wore in his last fight against Devon Alexander.
By Sunday it should become drier with spells of winter sunshine but temperatures will still remain on the cool side.