Both mum and baby are doing well after PC Robert Morgan helped with the delivery after being flagged down in the middle of his shift.
The new baby girl doesn't have a name yet but she's happy and healthy.
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The operation carried out by Westminster City Council led to the seizure of £8,000 worth of cigarettes.
Armed troops have been stationed around Parliament to free up armed police to patrol the streets in the wake of the Manchester bomb attack.
Chelsea had planned an open top bus tour to show off the Premier League trophy and hope to add the FA Cup in Saturday's final with Arsenal.