Like-for-like revenue for the 19 weeks to 8 May grew by 3%, with Total revenue up 2%.
The 60 strong chain of Grosvenor Casinos saw like-for-like revenue rise by 4% and Total brand revenue by 3%.
Grosvenor also saw a 35% increase in digital revenue compared to the same period in 2015.
“I’m pleased with the group’s performance during this 19-week period,” said Henry Birch, the group’s chief executive.
“We have seen continued like-for-like revenue growth across all of our brands and the performance in our Grosvenor digital business has been particularly encouraging.”
Mecca did not fare so well in the first five months of 2016.
Total customer visits were down 4% though largely offset by higher spending and like-for-like digital revenue dropped by 5%.
Like-for-like brand revenue increased 1%, but total revenue for the bingo chain dropped 1%.
Rank added it still expects “full year performance will be in line with management expectations”.
Shares in Rank jumped 9.6p to 247p.