Although deshifan is partly correct, I think one of the main reason as to why it swings more particularly in England is because during overcast it is much cooler than a normal warm sunny morning. Compared to the differences made by temperature and air pressure, humidity has a small effect on the air's density. But, humid air is lighter than dry air at the same temperature and pressure. I think the prime reason as to why it swings more is because of Colder air along with combination of greater atmospheric pressure.
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