Yes, processing times will vary depending on the staffing levels and working times.
However, the UKBA has stated generic Service Standards:-
For country specific information on processing times you can check here. The link gives historical data.Service standards
We have service standards for processing UK visa applications. Our standards say that we will process:
90 per cent of non-settlement applications within 3 weeks, 98 per cent within 6 weeks and 100 per cent within 12 weeks of the application date;
and 95 per cent of settlement applications within 12 weeks of the application date and 100 per cent within 24 weeks of the application date.
Please note that we define 1 week as 5 working days
Whether it's a good thing or not, there is no dark room in London to where all the visa applications are sent. (That dark room is reserved only for appeals against refusals)
In your case the applications would be processed locally by the Entry Clearance Officer(s) (ECO) based at the British Embassy in Dubai