I was assuming a 90% efficiency switching regulator to boost the battery voltage (taken as average 3.6V) to 5V for the Arduino. If it and your sensors are happy with a supply voltage varying from 3.0V to 4.2V without loss of accuracy, running them direct from the battery, saves a significant amount of power vs boosting to 5V, which I think accounts for the major discrepancy between our daily energy consumption figures.
That solar irradiance calculator uses insolation data from a 22 year period to give you the average insolation per calender month. You'd need to dig into its source data to find the worst December in that 22 year period, then look at Met. Office weather records to estimate how much worse the worst December in a 100 year period could be, and derate your expected 12.6Wh/day panel output accordingly. You'd also need the battery capacity to run for several weeks without recharge to make it valid to average your panel output over a whole month period, otherwise, if the UK experiences a succession of Atlantic winter storms, you need enough extra panel area to fully recharge the battery in the short spells of good weather between them, possibly only a day or two, despite any location and panel placement factors limiting insolation as Richard has mentioned
With a large enough battery, you may be able to make do with your panel in an optimal location if you drop back to reading at 30 minute intervals for approx 50% power saving if its below half charge.