The National Gallery was the second-most visited attraction in the UK, with 6.03 million people coming through its doors (up 14% on 2012).
The Natural History Museum came in third place (up 6.7% to 5.35 million).
And several other London attractions also saw big increases, including Kew Gardens (up 29%) London Zoo (up 26.4%) the Tower of London (up 18.4%) and the National Maritime Museum at Greenwich (up 27%).
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The 24-year-old was unarmed and the incident is not being treated as terror-related.
Some platforms have been taken out of service with disruption expected to continue until the end of the day.
The Met Office has extended its weather warnings for snow and ice to cover vast swathes of the country, including London and the South East.