Angies,
this is something that can be difficult to solve, especially as you have dry-lining which may mask some of the air-leakage points
have a look http://www.environ.ie/en/Publications/DevelopmentandHousing/BuildingStandards/FileDownLoad,18749,en.pdf (here) for some pointers and take a look at [broken link removed] best practice
some will suggest that you go around around with plenty of silicone and and expanding foam, but there is a limit to what can be achieved using this method.
its difficult to say for certain with out a survey and of course your budget has a lot to do with the results you'll get.
very few appreciate that a leaky house could easily have an air change rate of greater than 10 m3/(h.m2) at 50 pascals(where as a passive house is less than 1.0m3/(h.m2) at 50p) what all this means is not only are you feeling a draft but you also heating the air in your home as its on its way out..
changing your windows will help but if your doing this please consider installing them in a manor that reduces the thermal bridge around the opes and use a repeatable air-tightness tape.
can you tell me where in the country you are, as I may be able to recommend an architect &/or air-tightness tester to take a look (forget the BER assessor unless there one or both of the above)
here's a post (no. 20) that I wrote earlier, the reason I'm bring this to your attention is that - if you, by silicone, tape, membrane, External wall insulation or whatever means you choose, please note that you still require a ventilation strategy or you'll get excess condensation, mould etc. this means wall vents (which can have a draft reduction contraption put on them), window vents or a mechanical means (HRV or just Mechanical ventilation) must be adequately installed.