The entertainment PR agency was handed the account by Syco Music, the record label set up by X Factor judge Simon Cowell and a subsidiary of Sony Music Entertainment.
20-year-old Burke is releasing her version of Leonard Cohen's 'Hallelujah' and looks likely to make the Christmas number one spot.
The single went on sale on Saturday and has already become the fastest-selling download ever across Europe.
'We are currently dealing with hundreds of requests on a daily basis', said co-founder Simon Jones.
The agency has already given access to all the national newspapers and will be setting up interviews with weekly magazines before Christmas.
'In the new year we will sit down with Syco Music and work out a strategy for her PR, depending on the release date of the album', said Jones.
The agency is also handling PR for The X Factor 2009 Live Tour as a separate account.
Hackford Jones also looked after last year's winner Leon Jackson.