Ms Mellhi, 32, was born in British Sikh family, with her father and maternal grandparents hailing from India and her mother from Kenya.
The Daily Mail reported how she was in a Sainsbury's supermarket when she became aware of two people snickering in her direction.
She later found that two packets of pork scratchings had been placed in her basket.
Ms Mellhi believes this stunt could have an attempt to mock the Muslim religion because eating pork is forbidden in Islam.
"I think it was deliberate, though I couldn't say 100 per cent, but nothing about it was a normal situation," Mellhi told the Daily Mail.
"Did people want to offend me? I don't know. Did they think it was funny? Probably."
The BBC journalist has now taken this incidence to social media site Twitter: "To person who dropped two bags of pork scratchings into my basket in Sainsbury's: your pitiful Saturday activity backfired. I'm not Muslim."
“Had I been a Muslim or had it happened to a Muslim then I would have found it more offensive than I did.”
Ms Mellhi's Twitter followers have tweeted in her support.
