The environment agency have a tipping bucket rain gauge at Grimwith Reservoir that gives readings every 15 mins (but takes a couple of hours to update). Here's a graph of the recent data:
It's worth mentioning that TBRs have some reliability issues, specifically around high winds and frozen precipitation (snow/sleet/hail). The EA are installing heated TBRs in some regions to improve reliability but don't include this info on their API. They will tell you on request if the gauge you're interested in is heated (most are not).