Under new rules introduced by Facebook in October 2018, anyone placing a political advert must state who paid for it.
Since October, Mr Hollinrake has spent less than £100 on 36 Facebook adverts promoting constituency surgeries, parliamentary speeches and updates of his campaigning work.
The two adverts taken down were placed on March 7 and 8.
The first announced Mr Hollinrake was giving up single-use plastic for Lent, and the second was in support of the charity Rock 2 Recovery UK.
The MP’s social media team have confirmed the adverts were placed without a disclaimer due to an “administrative error” caused by confusing Facebook settings.
They added: “Kevin has asked we put systems in place to ensure it doesn’t happen again.”
The breach was discovered by JPI Media’s data investigation team, which found hundreds of individual MPs, elected officials and local authorities have placed nearly half a million pounds’ worth of promotions on the site in less than a year.
In the wake of the Cambridge Analytica scandal, last year the social media giant began publishing details of who places and pays for adverts promoting political or social issues.
Cambridge Analytica, a data analytics firm, harvested personal information from more than 50 million Facebook profiles without permission to build a system targeting voters with personalised political advertising.
Since Facebook began publishing details of political ads last October, spending has totalled more than £6.4 million.
And while much of the attention has focused on the big parties and pressure groups on either side of the Brexit divide, the data also reveals the thousands of adverts placed at a local level, often seeking to influence constituents on what can appear to be seemingly mundane neighbourhood issues.
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Under new rules Facebook introduced in October 2018, anyone placing a political advert must declare who paid for it.
The JPI Media investigation identified around 300 ads on the pages of local politicians and councils which were run without these disclaimers - including 40 placed on behalf of sitting MPs.
There is no suggestion that any of the adverts had been deliberate attempts to deceive constituents. They were all found and removed by Facebook.
But with a general election looking likely in the coming months, campaigners have questioned the transparency of the system.
The Open Rights Group, which campaigns for internet users’ digital rights, said social media has become a “key battleground for political campaigns”.
Its data and democracy officer, Pascal Crowe, said the “rules that shape our elections are ripe for reform”.
“For example, it is currently too easy to field a political advert on Facebook without revealing who is paying for that ad,” he said.
“It is now perhaps easier than ever to game the system and avoid being held to account."
A spokesperson for Facebook said: "Our industry-leading tools are making it easier to see all political ads on our platforms, and archives them for seven years in Facebook's Ad Library.
“People are able to report concerns to us or regulators as appropriate."
A Government spokesperson said: "There should be greater transparency in political advertising, which is why we have already pledged to introduce the requirement for digital election material to be clearly branded. We will bring forward technical proposals by the end of the year.”