Overseas residents made 6.99m visits to the UK, up five per cent from 6.684m a year ago.
The vast majority came from other European countries – 5.49m, up six per cent from 5.198m in the three months to April 2011.
Another 670,000 came from North America, up two per cent on the same period last year.
The jump in annual numbers was driven by a four per cent rise in both business travellers, to 7.3m, and those visiting friends and family, to nine million. Holiday growth was slower, at two per cent, to 12.2m.
Meanwhile, British residents made 11.84m visits abroad in the three months to April, up two per cent from 11.566m in 2011.
European destinations accounted for 8.62m of those, up one per cent from 8.578m last year, while 780,000 visits were made to North America, up four per cent from 749,000.
Overseas visitors spent £3.53bn in the UK in the three month period, while Brits spent £6.68bn abroad.