The mission advised those affected to contact the UK's anti-fraud line and said its officials have written to the UK Home Office, drawing their attention to the fraudulent calls.
"Indian nationals are advised not to entertain suspicious telephone calls and they should never part with their money in response to such calls," the mission said in its advisory.
It said that a number of incidents have come to the attention of the High Commission involving fraudsters having telephonically cheated some Indian nationals by posing as officers from the UK Home Office or immigration department or the UK Border Agency.
"In some cases, these fraudsters have also falsely claimed that they received such information about Indian nationals from the High Commission of India in London, other authorities in India, British High Commission in New Delhi."
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It has advised Indians in the UK to notify the local police and report the matter online to Action Fraud (www.Actionfraud.Police.Uk), by calling Action Fraud, or complain directly to their university or employer.
"I wish to inform all Indians living abroad that all such calls are fake. Plz inform the Indian mission. They will take up with the Police (Sic)," she tweeted in her response to the complaints.