What are some cheap (and landlord friendly) ways to fix a drafty flat?
If you have a draft then the best thing is to seal the source of the draft.  If this is a window, then as DA01 mentioned, you can install temporary plastic covers.  If it is around a door then you should look into replacing the weather stripping.  Also check visible gaps in the wall, floor, electrical and cable outlets - if they are drafty you can spray in expanding foam (e.g. Great Stuff) around the box (not inside).  Check outside too for visible gaps around openings.

You mentioned you closed up a vent - hopefully this was not a cold air return.  If the vent is the source of the problem then your best bet is to fill it in with rigid foam and seal the edges of the foam with caulking.

If the root issue is a lack of insulation in the walls then there is little you can really do that doesn't involve tearing up the walls.  Hanging long thick curtains along the wall might help a tiny bit.  I doubt tin foil will do anything besides making your friends suspicious.