We’ve just experienced a bitterly fought EU referendum involving highly divisive advertising campaigns by both leave and remain groups. Whether it was Vote Leave’s pledge to fund the NHS instead of sending £350m a week to the EU, its “Turkey is joining the EU” poster or the Treasury’s mailshot claiming UK families would be £4,300 a year worse off if Britain left the EU, there’s been controversy aplenty.

Had these been ads for products or services by commercial companies, we at the Advertising Standards Authority would have performed our usual role of holding to account the groups that ran them – checking the ads complied with the rules in the UK advertising codes, confirming they were legal, decent, honest and truthful.

The ASA has been making sure ads are responsible for nearly 55 years. But we’ve never applied the codes in full to political advertising, which we define as ads whose principal function is to influence voters in local, regional, national or international elections or referendums.

Given the more than 350 complaints we’ve just received from people about referendum ads, media commentators talking about a “regulatory gap” and online petitions calling for the establishment of an ASA-like body to monitor political campaigns (161,000 signatures and counting), there’s clearly a popular appetite for regulating political advertising. But there are good reasons why – at the current time – it cannot be the ASA that does the job.

Political advertising on broadcast media has always been banned, except for tightly controlled party political broadcasts. Until 1999 non-broadcast political advertising (which is allowed) was subject to some of the rules in the advertising codes. But only some of them: even then political ads were exempt from the rules that required all other advertisers to tell the truth.

That part-in/part-out approach was confusing and unsustainable. And so the Committee of Advertising Practice, the industry body that sets the rules, decided to exclude political advertising in its entirety from the ASA’s remit.

It did so for a combination of reasons, some related to the “special case” nature of political advertising. The short timeframes of elections made it likely ASA investigations would still be ongoing after the election had been held. The 1998 Human Rights Act raised concerns about restraining the freedom of political speech around democratic elections and referendums. And last but by no means least, the Conservative and Labour parties did not agree – despite encouragement from the CAP – to bring their political advertising wholly within the scope of the codes.

So here we are today with our curious status quo.

On the one hand, the overwhelming majority of big commercial companies support the ASA. They may fight like tigers if we rule against a particular ad, but our regulation of them without fear or favour coexists more or less happily with their general acceptance of the system.

On the other side, the majority of the main political parties have said they don’t want to subject themselves to the standards they expect of companies. There are good practical reasons for the ASA not playing a role, but the clincher is this: for a system like ours to stand a chance of working for political advertising, the starting point would have to be the clear support of the majority of political players.