The Electoral Commission is finally calling for an overhaul of electoral law to deal with the challenges of digital campaigning. The recommendations are welcome, but they are too little, and – from the point of view of alleged manipulation of the 2016 EU referendum – too late.

The Electoral Commission, as the “referee” of elections in the UK, is responsible for administering spending limits and preventing the kind of financial arms race that features in US elections. In making these recommendations for reform, the regulator is admitting what has been abundantly clear for some time: it lacks power.

It is calling for new powers to demand information, regarding, for example, spending on digital advertising, that it cannot currently access. It wants more transparency on what is spent by whom and greater powers to demand data. And inevitably, following the paltry £70,000 fine levied on Leave.EU in May, it is asking for higher maximum fines. Some of the proposals – such as the call to update “imprint” rules on the labelling of political ads – are not even new. The commission has been calling for this for years and it should be implemented with urgency.

But even if all of its recommendations were fast-tracked, question marks would still hover over digital and foreign manipulation of future elections, because the Electoral Commission has no remit to deal with the wider issues.

With our boisterous and partisan press, elections have never been walks in the park in Britain, but they have broadly permitted the political system to negotiate the conflicts of modern life – between rich and poor, capital and labour, centre and periphery. They have done so more or less successfully because the rules of the game were trusted, with our sense of fair play written into various areas of law as campaigns have evolved since the 19th century.

Alongside Electoral Commission rules, trust has been maintained by a political advertising ban on broadcasting, where most attention was focused, and impartiality rules for broadcasters. The big change going on now is the shift of political attention from such mass media platforms with a developed ethic of balance, responsibility and trust to a wild west that is open to foreign manipulation. None of this will be altered by beefing up a spending regulator.

It is parliament that is clutching the missing pieces of the jigsaw. The culture, media and sport select committee’s inquiry into fake news will be reporting later this year; it should not only support the Electoral Commission’s proposals, but widen them. Nobody wants to inflict an obligation to ration propaganda through party political broadcasts on Facebook, but the platforms must be encouraged – and forced if necessary – to think through the responsibilities that come with their sudden dominance in markets for political advertising. Data-driven message targeting requires a much wider review of the limits of acceptable behaviour in this new era of propaganda.

One of the problems with this is that parliamentarians themselves are increasingly involved in new forms of campaign on social media – the Electoral Commission reports that 43% of all campaign spending was on digital advertising in 2017. For example, it is individual MPs in the larger parties that benefit from the fact that spending on highly targeted advertising aimed at one particular constituency can count towards national rather than local spending limits (the former are much higher) – a move that the Electoral Commission wants to outlaw.

So the radical policy overhaul we need is likely to come from outside parliament, with the full involvement of civil society. We need a full-scale and independent inquiry into making our electoral law fit for the modern day and age. It must look at the entire system for political communication, including broadcasting and the press, and in particular the sensitive question of how to maintain maximum freedom of expression while also dealing with the potential for foreign manipulation. The Electoral Commission has said it wants more transparency regarding paid political advertising that may come from abroad. But it does nothing to approach the issue of organic (unpaid) campaigns from abroad, and the role of bots that may be located abroad. As part of the solution, social media companies – not only Facebook – should be encouraged to develop a new cross-industry code of conduct.

Competition between social media companies is not enough to get them to clear up their own stables. They need to be encouraged to do the right thing. We’ll only get there with a much more fundamental rethink of the system than the one the Electoral Commission is proposing.

• Damian Tambini is associate professor at London School of Economics and a member of the LSE Commission on Truth, Trust and Technology