Caving is always weather dependent and it is important to ensure that conditions are suitable before setting out on a field meet. Fortunately there are some resources which can assist caving parties to make some judgements in advance. The following sites show data provided by the Environment Agency for water levels on various rivers:
River Wharfe - Kettlewell
River Wharfe - Grassington
River Aire - Gargrave
River Nidd - Pateley Bridge
River Nidd - Gouthwaite
River Ribble - Langcliffe
River Ribble - Settle
River Wenning - Clapham/Ingleton
River Rawthay - Sedbergh
As always, use your own judgement but the above sites should help you to make an informed decision (coupled with knowledge of the flooding potential of the intended cave/pothole). Exercise caution if in the upper green area and it's probably best to forget it (unless a known dry trip) if in the blue area.
Additional resources:
UK national Water Guage & Webcam map
Yorkshire Dales Weather Forecast
Peak District Weather Forecast
Lake District Weather Forecast