When voters arrive at polling stations in the London borough of Tower Hamlets today, they will find a police officer. Police will also be patrolling polling stations elsewhere. For all the hue and cry about anti-aircraft missiles positioned on high-rise East End roofs, these measures have nothing to do with advance security for the Olympics. They reflect growing fears about electoral fraud. And there is room for considerably more alarm here than is apparent at the Electoral Commission – a watchdog with a remarkable propensity not to bark.

Not so long ago, this country was an acknowledged leader in the integrity of its democratic process, and we still send emissaries around the world preaching the benefits of well-run elections and observing flaws in other people's votes. We take a perverse pride in the simplicity of our secret, pencil-and-paper ballot and our manual counts. We see electoral fraud as something that happens in Russia and Zimbabwe, not in advanced countries such as ours.

This complacency is unwarranted. The British electoral process has weak points, which have become weaker over the years. One is the conspicuous laxness – by the best international standards – of our registration process; another relates to the huge rise in postal voting. Separately and together, these two shortcomings have raised doubts about the validity of the vote in some places. While the number of elections where the result has been found actually to have been rigged remains thankfully small, the extent to which elections have been influenced may well have been underestimated, along with the potential for manipulation in future.

True, the most obvious failures in the registration system are being remedied. Compared with, for instance, opening a bank account – where the identity checks often seem excessive – scandalously little is required of would-be voters. The say-so of a "head of household" suffices – with penalties advertised for those who fail to register everyone living at that address, rather than for those who register too many (which now seems the greater problem).

From 2014 – why so long? – each first-time voter will have to produce proof of identity and a signature to qualify for a vote. This has democracy campaigners worried that some of those entitled to vote – women in Asian households are cited – could be disenfranchised. Efforts must be made to prevent this. But the proliferation of phantom votes is a proven danger that has to be addressed.

If the good news is that this Government is trying to improve the registration process, the bad news is that it appears insouciant, to say the least, about the downside of increased postal voting. It was the last government that extended the right to a postal vote, in the hope of increasing turnout in general, and Labour turnout in particular. While a qualified numerical success, the bigger postal vote has created problems of its own. It is not clear that all postal voters actually exist or, if they do, are entitled to a vote. And it is all too easy for votes – real or fraudulent – to be "harvested" by supporters of a particular candidate, who may exert financial or clan pressure to secure their goal.

The Electoral Commission appears to have put little or no pressure on the Government to change this. And while the police and local authorities have been more assiduous in advance of today's elections about checking on multiple voters registered at one address, this is a costly remedy for a problem that would not exist if registration were harder and postal votes had not been distributed so generously. Some might say that it is to Britain's credit that we take the honesty of our elections for granted. Regrettably, that reflects a national naivety we can no longer afford.