The Border Agency ordered squatters to leave their makeshift homes in Hendon last month.
Dozens set up camp on a disused football ground, claiming they had nowhere else to go.
They were offered flights back home to Romania.
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A lamp in the tower which houses Big Ben is to be switched off for the first time in more than 70 years.
Sir Bruce entertained audiences for more than seven decades.
Work in the tower will also pause over the bank holiday weekend.