Its investigation into posts by Sophie Louise, Chloe Hill, Rae Eleanor and Amiie Giffen have been assessed, but closed because the posts fall outside of is remit.
"In these instances there was no commercial relationship in place between the brands and the influencers," ASA senior media relations officer Matt Wilson said.
"As there was no payment or reciprocal relationship in place and no editorial control of the posts by the brand, this is not classed as advertising."
Formal investigations are continuing into other complaints the ASA has received, including the promotion of Vype e-cigarettes by celebrities including Lily Allen.
A PRWeek investigation found that Big Tobacco used ‘earned social media’ as a marketing tactic to push its products onto consumers as traditional advertising is heavily regulated.
The ASA said other cases it is investigating involved Global Vaping Group, Attitude Vapes and Ama Vapes Lab.
ASA rules state that ads for e-cigarettes must be targeted responsibly; not be directed at under 18s through the selection of media or the context in which they appear; and no medium should be used if more than 25 per cent of its audience is under 18.
Crucially, people in ads promoting these products should not be, or appear to be, under 25. Last month, Philip Morris International suspended influencer marketing for its iQOS heated tobacco products after discovering an ambassador was under age.
Recently, PRWeek revealed that Facebook rules allow organic posts to promote tobacco products, including highly sexualised content advertising cigars. It’s a rule the social media giant says it will update in the coming months.
This week, health officials criticised a tobacco-industry-funded foundation over their PR spend.