BREXIT: This chart shows how critical undecided voters are for Britain to remain in the EU

Hannah Mckay / Reuters

Undecided voters are more likely to lean towards Prime Minister David Cameron and the Remain campaign.

There are just three weeks left until Britain votes on whether it should remain in the European Union.

That also means that time is running out for Britain's undecided voters to pick a side.

Importantly, a significant trend has started to emerge relating to undecided voters in opinion polls published over the last few weeks.

Since mid-May, the number of respondents who have told pollsters that they don't know how they intend to vote in June 23 referendum has been notably low.

In fact, since May 15, in not one poll have undecided voters accounted for more than 20%. The highest was 17% in a survey that YouGov published on May 24.

Where has the undecided vote been going? As Business Insider's chart below illustrates, in recent opinion polls where the number of undecided respondents has been notably low, support for Remain has been notably high.

Business Insider

The arrows point to examples of this trend. According to ORB and Ipsos MORI polls published on May 15 and 16, the number of respondents who said that they didn't know how they would vote was 5% (ORB) and 8% (Ipsos MORI).

Crucially, the same polls showed huge margins of victory for Remain. The ORB poll gave Remain a 15-point lead to Remain (55/4o%) and according to Ipsos MORI Remain was winning by 18 points (55/37%).

The same thing happened in an ORB poll published on May 29. A comfortable 9-point lead for Remain coincided with a really small number of undecided voters (7%).

This pattern indicates that something hugely significant could well be happening: Brits who were previously unsure about how they would vote in the referendum and starting to lean towards Remain.

If so, it wouldn't come as much of a surprise to most polling analysts and bookmakers. That's because is generally believed that voters who are unsure will typically opt for the status quo option as it's perceived as less of a risk.

As Matthew Shaddick, head of political betting at Ladbrokes told Business Insider last month: "In the history of these sorts of referendums, towards the end people usually opt for the safer option, and I think that will be the case this time around too."

With just a few weeks remaining until June 23, it looks as if the Leave campaign is losing the battle for the undecided vote which could prove vital in determining the outcome of the referendum.