Ugly partisan bickering is once again tainting the political parties as they seek to change a fundamental part of the rules governing general elections.

It's the way in which voters are registered that is being disputed. At the moment this is done via households. The coalition wants to switch to individual voter registration.

As Labour proposed this in 2009 but failed to get it implemented, you might think the shift ought to be fairly uncontentious. But after the brazen partisanship of the coalition's early bills meddling with the constitution, on fixed-term parliaments and the like, the opposition are now deeply suspicious of the Conservative and Liberal Democrats' motives.

They're justified in not trusting ministers an inch. According to research published last year the changes could result in as many as six million people falling off the register, when ministers had suggested the total would be far less. Labour is worried that many of these will be the poorer, inner-city sort of voters which tend to back their party come polling day. Not in their interests, therefore, that this change goes ahead. Tory constitutional reform minister Mark Harper insists there's a good chance the total number of registered voters won't fall at all.

After initial proposals were discussed in the last parliamentary session, the coalition's first midterm Queen's Speech earlier this month included the electoral registration and administration bill, which received its second reading yesterday.

I'll be following the details of the bill as it works its way through parliament. The coalition's proposals have only been subtly changed by ministers since Labour first kicked up a fuss about them last autumn. Here's a summary of the main changes:

  • The government had initially proposed offering voters a virtual 'opt-out' where they could say no thanks to voting with a simple tick of a box. Nick Clegg conceded that would be removed last year.
  • The main battleground then became the big gap between the final household annual canvass in autumn 2013 and the 2015 general election. Calls for a 2014 canvass were intense, but ministers weren't keen to cough up the extra money to pay for one. Now the autumn 2013 canvass is being moved to spring 2014 – a decent compromise.
  • The final big change is another compromise, over whether or not people who refuse to fill in the form have committed a criminal offence. There has been much head-scratching in parliament over this in recent months. Now the coalition has unveiled its answer: those not filling in the form will face a civil penalty of some kind, like a parking fine. Labour wants to know how much that fine will be, arguing this will make a big difference to its effectiveness.

So much for the detail. More compromises will undoubtedly follow in the months to come. But the big issue of party political advantage overshadowing the legislation is unlikely to be so easily resolved.

Labour's shadow constitutional reform minister Wayne David demonstrated this in his speech to the Commons yesterday. On the one hand, his arguments for the opposition amendment lamented the "breakneck" speed at which the change was being pushed through. Labour want the shift to go through as slowly as possible, with the Electoral Commission doing all it can to minimise the number of voters who get lost in the process.

If Labour were to stick to such arguments and ignore the party political side of this they might improve their credibility. But they cannot resist trying to foment Lib Dem dissension by voicing their concerns about the partisan nature of the changes.

The problem relates to another contentious coalition constitutional reform – boundary changes. The next review is set to begin in December 2015, exactly when – Labour fears – the number of people registered on the list could be at its lowest.

"I do not think it is mere coincidence," David warned darkly. "It is possible to look at the dates and come to certain conclusions. I only wish that the Liberal Democrats would do the same and recognise that there is a lot in what I say."

Labour's fear is that the entire electoral map of the country could be reshaped as a result of the electoral register. All those lost Labour voters will be simply forgotten about.

The problem goes beyond a few safe Labour seats being eaten up. It has a wider negative impact, undermining Ed Miliband's chances of becoming prime minister at the next general election.

At second reading Labour's amendment to reject the bill was defeated by 283 to 223, a fairly standard coalition majority of 60. The bill will now move to detailed line-by-line scrutiny in committee. As it does so it's unlikely that the fundamental suspicions of Labour will be erased. As the bill progresses the sense of partisan game-playing as an unpleasant subtext is only going to intensify.