I know your aware of the deadlines and i'm unsure how the firms will react to your application - i'd imagine they'd treat you the same as everyone else. You might as well apply to the bigger firms first as they are the ones who'll be more picky... the mid-tier/small firms may be much more receptive to you and thankfully you can go through the big firms interview process before you need even apply for the smaller firms.
The following list of deadlines might be of interest to you (firms ranked by fee income)...
PWC - 23rd October
KPMG - 23rd October
Deloitte - 23rd October
E&Y - 23rd October
BDO - 24th October
Grant Thornton - 24th October
FGS - 14th November
Mazar - 23rd October
RBK - 14th November
Horwath Bastow Charleton - ???
Baker Tilly Ryan Glennon - 14th November
HLB Nathans - ???
OFC - 21st November
OSK - 14th November
Plus theres plenty of smaller regional practices with graduate programmes with no explicit deadline or much later ones... Mulhern Ryan, Gilroy Gannon, MA Stephens, Kinnear, CrowleyDFK (Dec 12th), JP Greely etc...