Before spending anything on windows, look at what hangs in front of them. A good pair of lined curtains, drawn at the right time, traps a layer of still air against the cold glass and cuts the heat a window loses overnight. It is about the cheapest insulation there is, and most of it is in how you use what you have.
Why they work
Glass is a poor insulator, and at night a window radiates your heat straight out. A heavy, close-fitting curtain creates a pocket of trapped air between fabric and glass that slows that loss, much as secondary glazing does, only softer and cheaper. Thermal-lined or interlined curtains do this far better than thin unlined ones, and the heavier and more closely fitted they are, the more they hold the warmth in the room.
The timing trick
The habit matters as much as the curtain. Draw them at dusk, before the evening chill sets in, to keep the day's warmth inside, and open them fully in the morning. On a sunny winter day, open curtains on south-facing windows let free solar warmth flood in, so the rule is closed against the cold and dark, open to the sun. Done consistently, this single routine noticeably steadies a room's temperature for no cost at all.
Hang them to seal
A curtain only traps air if it fits closely. Curtains that reach the floor and overlap in the middle hold heat far better than short ones that stop at the sill with gaps down the sides, where warm air spills out and cold tumbles in. A pelmet or a deep rail across the top stops the chimney effect of air rising behind the curtain. The closer the fit all round, the better the seal.
Never trap the radiator
The one mistake to avoid is letting long curtains hang over the radiator beneath the window. That funnels the radiator's heat straight up the cold glass and out, exactly where you do not want it. Either tuck the curtains behind or onto the windowsill above the radiator, or use sill-length curtains there. Keep the heat coming into the room, not channelled out through the window.