The Olympic Park in Stratford has closed to visitors as the site is prepared for the start of the Games in a few weeks.
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The mayor went on a walkabout at a farmers market in Bedford and signed copies of his new book in a local book store.
People are being encouraged to post pictures of themselves sleeping in "weird" places in a bid to raise money to tackle homelessness.
The actor received the award at Guildhall in recognition of his work for gay rights.