Crossbench peer the Earl of Clancarty asked the Government whether the Home Office would review the 18-year-old singer’s case "to ensure that she is allowed a visa to continue her stay in the United Kingdom".
But he received a letter from the UK Border Agency insisting the decision – made because her mother wrongly claimed state benefits – was correct.
Nhengu’s case has been met with an outpouring of public support, after it emerged the teenager faced deportation to her homeland because her mother’s visa application has been turned down.
Nokuthula Ngazana was permitted to stay in the UK while she studied at university, with Nhengu permitted to remain in the country as her dependant.
But Ms Ngazana’s application to remain in the country was turned down, with the UK Border Agency saying she had "obtained public funds for which she is not eligible".
In the letter to Lord Clancarty, a UK Border Agency official said: "Miss Nhengu is here as the dependant of her mother. Her mother applied out of time for leave to enable her to continue working here but this application was refused, without the right of appeal, because she had obtained public funds for which she was not eligible.
"The mother’s visa clearly stated that she was not eligible to receive public funds and a comprehensive list of the relevant public funds is available on our website.
"I am satisfied that the decision to refuse the mother’s application and to refuse her dependants in line was the correct one."
Lord Clancarty said he was surprised by the tone of the letter, adding: "Clearly there is a section of the public who would wish to see Gamu stay here."