Coronil, a herbal remedy from India, was found on sale in shops in predominantly Asian areas across the capital.
Manufacturers Patanjali Ayurved claim the pills protect against "respiratory tract infections".
Tests carried out for the BBC show the pills offer no protection from coronavirus.
A lab test of the drug carried out by Birmingham University for the BBC showed the pills contained plant-based ingredients which cannot protect against Covid-19.
Virologist Dr Maitreyi Shivkumar said the idea of "boosting" immunity makes no sense in terms of treating coronovirus.
"There are lots of nuances in how our immune system responds to the virus. We do not even know that heightening immunity helps," she said.
"It is unclear what Coronil is trying to do to the immune system."
UK advertising rules ban references to Covid-19 and "boosting immunity".
Similar claims are permitted in India, where Patanjali Ayurved has a large following.
One shop in Wembley advertises Coronil as a "Covid-19 immunity booster" both in store and on its website.
The BBC has located at least four other stores that sell the pills, claiming they treat Covid-19.
One customer told the BBC: "I take it because I'm 78.
"If I go out shopping I could catch coronavirus from anybody. That's why I take it… to protect myself."
There are no authorised health claims in the UK that any substance can "boost" immunity, according to the Advertising Standards Authority (ASA).
Claims to prevent, treat or alleviate the symptoms of coronavirus cannot be made without a product being licensed by the Medicines and Healthcare products Regulatory Agency (MHRA).
The MHRA, which has not approved Coronil for any use, said: "Appropriate action will be taken where any unauthorised medicinal product is offered or sold on the UK market."
Patanjali Ayurved founder Baba Ramdev claimed in June that Coronil had cured Covid-19 patients.
"Our medicine resulted in 69% of coronavirus patients testing negative after three days and 100% after seven days," he said.
The Indian government has said Patanjali Ayurved can market Coronil as an immunity booster but not a cure.
Patanjali Ayurved has now withdrawn its claim that Coronil is a cure for Covid-19.
According to Full Fact, an independent fact-checking organisation, "misinformation like this can cause harm to people's health and finances".
Abbas Panjwani, a researcher at Full Fact, said: "During a pandemic, it is natural and perhaps understandable for people to seek out answers."