Surely to a first approximation, the length of a day in London is roughly:

length (hours) = 12 - 4.17 x cos(2xPI x day/365)

where "day" is the number of days from the shortest day (21 Dec).

(the factor 4.17 gives a shortest day of 7hr 50mins, the factor would get bigger as you go further north)

I've no doubt this is a bit of a simplification, and will break down as you get too close to the arctic circle...

However it will be apparent that near the spring and autumn equinox the cosine function is passing through zero, where it has its steepest gradient, so the rate-of-change of length-of-day will be maximum.