For Ladbrokes, this is weighted at 81 per cent in favour of Remain, while Leave is weighted at 19 per cent. William Hill, however, which does not remove its margin on bets, weights these odds at 86 per cent in favour of Remain and 25 per cent in favour of Leave.
The Remain camp has also been handed the lead in the final Brexit polls released today. However, Ladbrokes emphasised the Brexit camp has rallied slightly from earlier in the day, rising from 14 per cent, according to the bookmaker.
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Alex Donohue of Ladbrokes said: "Remain rallied in the early trade but as the afternoon wears on the support for Brexit is growing.
"Leave backers didn't seem to get the memo that the market was calling this as over and it now looks a certainty to go on long until the night."
Largest political betting event in history
Betfair's odds as of 17.45pm (GMT) are currently 84 per cent in favour of staying in Europe, down from a day-high of 90 per cent at midday today, though up from a range between 60 and 67 per cent by the end of last week.
The latest odds for Remain are 2/11, while Leave is 5/1 at 16 per cent.
A spokesperson for Betfair said more than £63m has now been traded on its market, making it the largest political betting market in the bookmaker's history. The previous biggest political betting market was the US election in 2012, which traded £40m.
The Remain camp currently wins the prize for the single largest bet, at £315,000, according to Betfair, while the largest Leave bet has been £194,000.
Scotland currently has the highest proportion of people backing Remain, with 64 per cent of Scottish-based bettors betting on a vote to stay in the EU, while the East of England at 55 per cent and Guernsey at 57 per cent have the most bets placed on a Brexit vote.
Betfair spokesperson Naomi Totten said:
The sheer volume of money being traded on this market is phenomenal with over £63m now matched and £12m of that being traded today alone.
The largest betting market in Betfair Exchange history is £102m on a World Cup cricket match in 2015. It is unlikely that the Brexit market will surpass that, but we are predicting that it will sit comfortably in the top 10 markets of all time.