The Met office have finally followed through on their threat to Web 2.0 their Mountain-Safety website (boo hiss), so it doesn't work over WAP or with 'dumb' phones:
http://www.metoffice.gov.uk/public/weather/mountain-forecast/#?tab=mountainHome

However, they've also launched a load of specific hill + fell forecasts:-

i.e. Leck Fell
http://www.metoffice.gov.uk/public/weather/leisure/#?tab=leisure&map=POI&zoom=9&lon=-2.52&lat=54.20&locId=354844&fcTime=1416441600

Some caving hills / areas are "Places of interest", some are "Sports and outdoor recreation".

In Yorkshire we appear to have:-
Leck Fell, Ease Gill, Long Churn Cave, Ribblehead

There's a lot of information there, and in the lower-right there's the altitude information for the reference point.