Since you are renting I doubt you could replace them without the landlord's permission, but what are indeed called "mixer taps" are available from any builders-merchants or stockists of plumbing materials.
They are not attachments on the existing taps though, as I think you are asking for but are very unlikely to find.
Instead a mixer-tap is a complete fitting combining both taps in one unit, fed from both the hot and cold water pipes. They are very common on kitchen sinks, perhaps less so on washbasins.
Anyway separate taps are no more or less "useless" in Winter than mixer-taps, provided they and the pipework are protected from freezing. If that is the problem, you need have the pipes lagged properly.
