Renting does not mean you have to put up with a cold flat. Many of the best draught-proofing fixes need no drilling at all, and you can take them with you when you move.
Zero-damage fixes
Loose draught excluders. A fabric excluder laid along the bottom of a door leaves no mark and moves with you.
Twin-sided covers. A sleeve of foam or fabric that slides over the bottom of the door. No adhesive, no tools.
Wool chimney pads and balloons. A chimney draught excluder pushes in by hand and lifts out. Only for unused chimneys.
Letterbox catchers. Some fit with adhesive and peel off again.
Low-damage fixes
Self-adhesive silicone sweeps. A sweep stuck to the bottom of a door can be removed by warming it and peeling slowly. Test a small hidden spot first, since old or flaking paint can lift.
Clear window tape. A clear seasonal tape over the gaps around a sash is designed to come off without residue, but test first.
Foam tape. Self-adhesive foam tape on a frame will usually peel off, though foam can leave a sticky mark that a little white spirit removes.
Ask first
Brush strips that screw to the door, replacement letterplates and window seal replacements involve drilling or changing fixtures. Ask your landlord. Many are happy to approve a simple improvement that makes the property warmer, particularly if you offer to pay.
Fire doors
Flats often have fire doors, and landlords have legal duties around them. Do not drill, trim or fit anything to a fire door without your landlord's written agreement.
Keep the paperwork
Take photos of the door and window before you fit anything, and keep the receipts. If you need to remove a seal at the end of the tenancy, photos help show the finish was unchanged.
Take it with you
The best renters' kit is portable: a couple of fabric excluders, a roll of clear tape and a chimney pad. When you move, they go in a box.