Polling stations have been flooded in areas including Kingston and Worcester Park, and one voter said they had to be "carried in" as torrential downpours swamped parts of London and the South East.
The fire brigade has been inundated with more than 300 emergency calls.
Voters are going to the polls to decide whether the UK should remain in the European Union in a historic moment for the future of the country.
People tweeted that some polling stations had been relocated due to the weather but many were "packed" as they opened at 7am this morning.
These 11 voters were not deterred by the weather:
Nigel Farage, the leader of Ukip who supports a Leave vote, had said he believed those voting 'Out' would "crawl over broken glass" to get to the polling station.
These seven voters thought the scene in the early hours this morning suggested a high turnout could be on the cards:
Polling stations across UK
The polls in the run-up to the big day have suggested the referendum result is on a knife-edge, with neither side able to surge ahead in the final weeks.
Both sides of the referendum campaign have been locked in fierce fighting for months, and things came to a frenetic close on Wednesday as senior politicians travelled across the country to try and sway undecided voters.
The Remain campaign, led by David Cameron, has repeatedly stressed that the UK is “stronger, safer and better off” inside the EU, The Press Association reported.
The Prime Minister and his Remain colleagues from across the political spectrum have also warned of the potentially severe economic consequences of a Brexit vote amid fears of financial market turmoil and another recession.
But Leave campaigners, led by Tory heavyweight Boris Johnson, have urged voters to “take back control” of the country.
Leave campaigners believe a divorce from Brussels would give the UK more money to spend on national issues like funding the NHS as well as giving the Government the ability to control the nation’s borders and levels of immigration.
Mr Johnson has suggested that June 23 could be remembered as the UK’s “independence day”.
The referendum campaign has been punctuated by ill-tempered exchanges and interventions with both sides accusing the other of scaremongering, particularly over the issues of the economy and immigration.
Nigel Farage came in for particularly stern criticism after unveiling a Brexit poster showing a queue of hundreds of immigrants arriving in Europe with the slogan “breaking point”.
And Leave campaigners were left furious after George Osborne made use of Treasury research to warn that quitting the EU would result in households being £4,300 worse off.
Meanwhile, dozens of celebrities have intervened during the course of the campaign to make their feelings known.
Footballer David Beckham, James Bond actor Daniel Craig and Harry Potter author JK Rowling were just three of the high profile names to back the Remain campaign, while Leave won support from the likes of comedian John Cleese, former cricketer Sir Ian Botham and former England football player Sol Campbell.
A record number of voters are eligible to take part in the referendum with the Electoral Commission putting the number at 46,499,537.
A last-minute surge to register crashed the Government’s website hours before the deadline on June 7, prompting a 48-hour extension.
Polling stations opened at 7am and will close at 10pm.