And while things aren't expected to improve much over the next 24 hours, there is good news as we go into the weekend.
Met Office forecasters are predicting sunshine to finally return on Saturday afternoon with temperatures creeping back up towards 20C.
The brighter and drier conditions are expected to last through Sunday and into Monday.
The full Met Office forecast for Yorkshire
Rather cloudy, cool and damp, with a northerly breeze, extensive low cloud and spells of rain. The rain will be heaviest first thing, gradually becoming lighter and more intermittent as the day goes on, with winds falling light. Maximum temperature 16C.
Remaining generally cloudy and damp overnight, with a little further rain. Some lengthier drier spells should develop as the night goes on. Minimum temperature 12C.
Another damp and rather cloudy day, with hill fog remaining extensive as a northerly breeze re-develops. Further mostly light spells of rain are expected, perhaps becoming heavier during the evening. Maximum temperature 18C.
Outlook for Saturday to Monday:
A much brighter, warmer few days: Saturday mainly dry with some warm sunshine ahead of rain later. Breezier Sunday, but with some sunny spells. Fine again Monday but cloudier later.