That said, one in six people have still not made up their minds.
But for 'leave', there is also the hurdle of the strict limit on spending that disadvantages them.
The formal 'leave' and 'remain' campaigns each have up to £7m to spend, access to TV broadcasts, and one free mail to each household in Britain.
But on top of that, parties can also individually support campaigns with caps of £7m each for the Conservatives and Labour, £3m for the Liberal Democrats, £4m for UKIP and £700k each for the SNP and the Greens.
That pits up to £11m for 'leave' against up to £18.4m for 'remain' (since the Conservatives are officially neutral).
This might sound like a lot of money but is comparatively small beer when one considers the momentous nature of the decision being made and the context of spending on US presidential election campaigns, likely to top $5bn this year.
So if 'leave' campaigners want to win they need to get creative. The 'remain' campaign has probably run the best campaign, so far at least; managing to use the Prime Minister’s influence to persuade US President Barack Obama to speak up during his recent trip to the UK.
Besides Boris Johnson – a charismatic no-nonsense figurehead for 'leave' – its campaign has displayed limited star power.
It also seems to be attracting some choice overseas supporters of Brexit, including French National Front chairwoman Marine Le Pen and Donald Trump.
For 'leave', it would be wise to petition public support for a TV showdown as soon as possible. From polling voters, we know a TV debate in a prime-time slot is one of the most effective ways to sway thinking.
But this kind of head to head has yet to be confirmed, if it happens at all. Part of the reason it’s unlikely is because voters are so influenced by just the look of people, the soundbites, who’s sweating the least.
That was why in 2015, the Conservative Party did its best to water down the format by including as many contending voices as possible.
It’d be a mistake to copy 'remain' with its controversial household leafleting campaign. It did the job of looking like impartial government advice, but who read it?
Targeted advertising online is likely to feature strongly in both campaigns soon – with 'leave' needing to target grey voters who are more Eurosceptic and more likely to vote.
We’ll also see many independent campaigners, not officially in either camp, but able to use their own sources of money to air more extreme views.
'Remain' needs to continue to keep the media on-side (what’s happened to all the Euro-bashing from all sections of the press?), avoid complacency, and work up a much more positive narrative for staying in the EU – only hope trumps fear, and that requires a positive story that neither have yet offered.
Paul Baines is professor of political marketing at Cranfield University School of Management