For carbon dioxide (CO2) the answer depends largely on the carbon content of the waste. Burnley  reported, based on Environment Agency data, an average percentage of carbon in UK waste of 34%.
If 1 tone of UK waste contains 340 kg carbon, as Burnley suggests, then assuming complete burn-out was achieved it would release approximately 1,246 kg carbon dioxide (340 x 44/12).
There will also be some nitrous oxides and other Greenhouse Gasses (GHGs) but much smaller levels.
Eunomia  says: Nitrous oxide is a GHG which is 310 times as potent in terms of radiative forcing (though actually, this depends upon the time horizon adopted). It is believed to be more of an issue where combustion temperatures fall below 850C and where the control of NOx is through use of SNCR, especially with urea as the reagent. Authoritative data on N2O emissions is difficult to come by. The Bref note for Incineration suggests a range for municipal waste incinerators of 1-12 mg/Nm3, which would translate to (roughly) 5g 60g per tonne of waste.
 Burnley, S. J. (2007). “The use of chemical composition data in waste management planning – A case study.” Waste Management 27(3): 327-336.
 Hogg, D. and Eunomia Research & Consulting Ltd (2006). A changing climate for energy from waste – Final Report for Friends of the Earth, available from http://www.foe.co.uk/resource/reports/changing_climate.pdf