The latest International Passenger Survey found that the number of overseas visitors had increased by 9%, to six million people, in the three months to April compared with the previous quarter.
But the figures were still 3% lower than the same three months last year, before foot-and-mouth had begun to take its toll on visitor numbers.
The industry had yet to recover from that blow, the Office for National Statistics (ONS) figures showed.
For the year to April, overseas visitor numbers were down by 8% compared with the year before.
The number of visits abroad by UK residents in the three-month period was up 3%, to 14.9 million, compared with the previous quarter and up 2% against the same period last year.
The ONS figures are broadly in line with British Incoming Tour Operators Association statistics published last month.
These suggested the number of foreign tourists coming to the UK in April was still down on last year, but slowly recovering.