As a rented house, the things you can do at modest cost are:
look in the loft and see if it has ten inches (yes ten) of insulation. If not, you can probably get it fitted at subsidised or free deal through your gas or electricity suppler
draft-proof the doors and windows. Use the rubbery strips, not plastic foam. It will not stick to dirt or to rough flaky paint, but sticks very well to clean new gloss. Get a flap for the letter box.
The temporary plastic film that goes over windows really does work. The sticky tape will not stick to old rough paint... etc
keep your internal doors shut
if you have any fashionable bare floorboards, they will be cold and draughty. Cover as much as you can with rugs or carpets
Look at the hot pipes around your boiler and cylinder. They should be insulated. If you have a hot water cylinder and it does not have a factory coating of rigid foam, buy two red jackets and wrap it up.
It might be interesting to know the name and number of your boiler.