More than 6.7m visits in 2013, including busiest month ever in July, surpasses previous record of 5.9m in 2008

In 1759, around 75 people a day would trickle to the newly opened British Museum to see the array of remarkable exhibits, everything from the skull of a rhinoceros hornbill and a Dürer watercolour to a model of the church built on the site of the crucifixion.

Last year visitors flocked to the museum and on its busiest day there were 33,848 people, the museum said on Tuesday as it announced record annual visitor numbers.

In 2013 there were 6,701,036 visits, beating the previous record of 5.9m in 2008 and up 20% on 2012. The busiest day of the year was Friday 16 August – it was raining – and the busiest month ever was July, with 747,936 visits.

The figures were announced on the eve of what will be the 255th anniversary of the British Museum opening to the public.

Neil MacGregor, director of the museum, said he was delighted that so many people visited in 2013. "Displays onsite, loans and touring exhibitions nationally and internationally, big-screen viewings and online access mean this is truly a dynamic collection that belongs to and is used by a global citizenship."

A spokeswoman for the museum said 2013 had seen a particularly well-received programme of one-off exhibitions. Life and Death in Pompeii and Herculaneum was seen by more than 471,000 people, achieving its original visitor target of 250,000 in the first half of its six-month run. It now ranks as the third most popular exhibition, although it's still some way behind the Tutankhamun fever of 1972 (1.6m) and China's terracotta army in 2007 (850,000).

Other successful shows were the Shunga erotic Japanese art exhibition, which had 87,893 visitors in three months, and ice age art, which had more than 90,000 visitors more than double the target of 40,000.

The spokeswoman said the museum, like other national museums and galleries, had benefited from a "post-Olympics bounce". While 2012 tourist levels were high, people were more likely to be going to the Olympics than a museum.

A higher proportion of UK residents also visited the museum. In 2012 the overseas/UK ratio was 75% to 25% while in 2013 it was closer to 60% to 40%.