The UK Environment Agency issued a number of flood warnings and at least 22 flood alerts across the south-east of England, causing significant traffic pile-ups and queues at some polling booths.
The projected results, meanwhile, remained largely on a knife-edge as most opinion polls have been too close to call.
A rumour circulating on social media was claiming that the Remain campaign is trying to "rig" the election by rubbing out votes cast in pencil.
"When you fill in your #EURef ballot paper on Thursday, you can use a pen or the provided pencil - it's your choice," it tweeted.
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The four-month campaign has seen some of the mosthighly-charged in UK electoral history,throwing up deep divisions within the ruling Conservative party.
The Remain camp, led by British Prime Minister David Cameron, have been accused of using fear of economic consequences to argue their case.
The Leave side, in arguing against the status quo, have asked the public to vote to take back control of the UK's borders and finances.
A "Breaking Point" poster, described as "vile" by all sides of the debate, issued by far-right UK Independence Party (UKIP) in the last few days of the campaign was a blatant attempt to whip up public frenzy over the EU's freedom of movement rules.
While the UK has remained fairly divided, there is a clear "Vote Leave" heartland in the northern counties and the east coast of Britain, with "Remain" strongholds being the cities of London, Edinburgh and Bristol.