There's a number of ways to warm up old & draughty windows, including several kinds of secondary glazing. Shrink-wrap plastic film works quite well, especially when combined with draughtproofing brushes. 

Another option, especially if you (or your landlord) are willing to make a bit more of an investment is secondary glazing made from self-adhesive magnetic strips and perspex. It seems to be a very elegant and convenient solution to draughty/single glazed sash & cash windows as the panels fit over the window frame and can be easily removed in summer. You can find more information about the kits here

http://www.magnetick.co.uk/gbu0-prodshow/diy-secondary-glazing-magnetic-double.html

http://www.indigoshop.co.uk/gbu0-prodshow/magnetic-secondary-glazing-kit.html

We'e just installed some in our house. We bought the kits and perspex sheeting (which can be cut to order) from Easter Road Plastics (now no longer on Easter Road!) - the kits were on discount so only £30 for 30 metres of magnetic strips! You can find their address here:

http://www.applegate.co.uk/all-industry/easter-road-waste-scrap-non-agricultural-wholesale-1107946.htm