Gordon Brown and his cohorts at have the lead over actor and comedian , whose odds sit at 6/5, and controversial comic and radio host , who is at 8/1.
Among the other political users, London mayor is 40/1, while the sit at 80/1.
BBC presenter has better odds at 10/1, while Scottish singing sensation Susan Boyle is an 80/1 outsider.
Darren Haines, UK PR manager at Paddy Power, said: "Twitter could be the only popularity contest this government looks likely to win -- although it wouldn't be the first time this year they have been declared the nation's biggest twits."
Separately, Paddy Power has given actor Ashton Kutcher the best odds to become the world's most popular Twitter user this year. Kutcher sits at 4/6, followed by singer Britney Spears at 3/1 and CNN Breaking News at 12/1.
UK's Most Popular Twitterer in 2009:
11/10 Downing Street (DowningStreet)
6/5 Stephen Fry (StephenFry)
8/1 Russell Brand (RustyRockets)
10/1 Jonathan Ross (Wossy)
16/1 John Cleese (JohnCleese)
18/1 Phillip Schofield (Schofe)
20/1 Alan Carr (AlanCarr)
25/1 Jamie Oliver (Jamie_Oliver)
33/1 Charlie Brooker (CharltonBrooker)
40/1 Boris Johnson (MayorOfLondon)
50/1 Andy Murray (Andy_Murray)
80/1 Conservatives (Conservatives)
80/1 Susan Boyle (SusanBoyle09)
150/1 Paddy Power (PaddyPower)
200/1 Kelly Brook (Kelly_Brook)
Most Popular Global Twitterer in 2009:
4/6 Ashton Kutcher (Aplusk)
3/1 Britney Spears (BritneySpears)
12/1 CNN Breaking News (CNNbrk)
14/1 theellenshow (TheEllenShow)
14/1 Barack Obama (BarackObama)
16/1 Twitter (Twitter)
18/1 Jimmy Fallon (JimmyFallon)
20/1 Perez Hilton (PerezHilton)
20/1 iamdiddy (IAmDiddy)
20/1 Coldplay (Coldplay)
33/1 Demi Moore (MrsKutcher)
33/1 Al Gore (AlGore)
33/1 Ryan Seacrest (RyanSeacrest)
40/1 The New York Times (NYTimes)
40/1 Lance Armstrong (LanceArmstrong)
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