The library has been placed alongside the likes of the National Gallery and Southbank Centre in the list drawn up by the Association of Leading Visitor Attractions (ALVA).
It is tenth on the prestigious list after attracting more than 2.4 million visitors in a year – significantly ahead of London’s British Library, which drew 1.6 million visits.
This comes amid mannoth cuts to the £188 million library which will see its opening hours reduced from 73 to 40 hours per week – significantly below the others on the list.
The library is now making more than half its staff redundant as part of council budget cuts.
London’s British Museum continues to be the most popular visitor attraction on the capital-dominated list.
Edinburgh Castle and Chester Zoo are the only other non-London attractions in the top 20.
Museums and galleries across the UK saw an increase of more than six per cent on visitor numbers on the previous year, researchers said.
The Top 10
The British Museum: 6.7m
The National Gallery: 6.4m
Southbank Centre: 6.3m
Tate Modern: 5.8m
Natural History Museum: 5.4m
Science Museum: 3.4m
V&A, South Kensington: 3.2m
Tower of London: 3.1m
Somerset House: 2.5m
The Library of Birmingham: 2.4m