Celebrities who promote products on social media are under investigation by the competition watchdog amid concerns they are not making it clear when they have been paid to do so.

The Competition and Markets Authority (CMA) is looking into whether consumers are being “misled” by so-called social media influencers, who can earn tens of thousands of pounds from companies for a single post.

It has written to at least 10 celebrities who it said “can sway the shopping habits of millions” to ask for more information about the deals they have struck to promote certain brands.

The CMA, which has the power to fine or even imprison people who persistently breach consumer law, said it had seen examples of celebrities promoting products or experiences without disclosing that they were advertising in exchange for a fee.

 High-profile influencers on social media sites such as Instagram typically use the hashtag #ad to disclose when they have been paid to post about a product. But the CMA is understood to be telling celebrities that the existence of a commercial relationship must be immediately clear upon viewing the post, meaning the hashtag may not be enough.

A search of Instagram by the Guardian found several influencers, including a contestant from a reality TV show, endorsing items including ice-cream, stationery and clothing, without using the hashtag prominently, if at all. It is unclear whether they were being paid to do so.

George Lusty, the CMA’s senior director for consumer protection, said: “Social media stars can have a big influence on what their followers do and buy. If people see clothes, cosmetics, a car, or holiday being plugged by someone they admire, they might be swayed into buying it.

“So, it’s really important they are clearly told whether a celebrity is promoting a product because they have bought it themselves, or because they have been paid or thanked in some way by the brand.”

The celebrities – the CMA said it could not name them – are expected to be called in for interviews as the investigation continues. The watchdog is also asking the public to share their experiences and said it was particularly interested in hearing from anyone who had bought products endorsed on social media.

Typically, celebrities and influencers have millions of followers who watch their channels to see where they go on holiday, what they wear, which products they use, the books they read and more.

Some of the best-known influencers do flag up their commercial interest when promoting products.

One Instagram photo by David Beckham for watch company Tudor, which has been liked more than 1.7m times, admits to the existence of a paid partnership, while a picture posted by Cara Delevingne on her Instagram account, which is closing in on 1m likes, uses the hashtag #Ad.

Alfie Deyes, half of a UK social media power couple with fashion and beauty vlogger Zoella, posted a picture of himself on Instagram juggling small pots of Nutella, including the #Ad hashtag. It attracted 169,000 likes.

Paul Crockford, an agent for musicians and athletes, said the most well-known stars could earn huge sums for a post. “It you’re an elite football player, Premier League and international for instance, you can get £100,000 for a single post.”

Such online endorsements can help brands reach target audiences and boost sales, particularly among young people who engage less with traditional forms of marketing such as TV advertising.

In one example from this year, the London-based fashion label Kitri sold out of its £145 Gabriella dress in under an hour, shifting 200 units after a fashion blogger posted a picture of it to her 344,000 Instagram followers.

But influencers must make clear in such posts that they have been paid or rewarded to promote, review or talk about a product under the Consumer Protection from Unfair Trading Regulations 2008.

This year, the Advertising Standards Authority also launched an investigation into advertising by influencers after a surge in complaintsabout the practice. It issued a string of rulings against minor celebrities for failing to disclose they were being paid to promote products, including the former Hollyoaks actor Stephanie Davis, who used her account to promote a vitamin company.

Another case last year involved the online makeup Instagram blogger Sheikhbeauty, who promoted Flat Tummy Tea, described online as a herbal detox tea.

In December last year, the blogger wrote: “@flattummytea 20% off guys!!!! If you’ve been following me you’ll know i used this and I genuinely feel less bloated and a flatter tummy … oh yessss.”

Crockford said there was a “grey area” for stars who had long-term promotional deals and may unwittingly post pictures featuring the brand in question. “If you’re a footballer sponsored by Lucozade and you post a training picture with a bottle somewhere in the background, do you then have to say you’re sponsored?”

“There has to be some common sense.”