The longest and shortest days of the year are those with the greatest and least amount of daytime. They occur at the time of the solstices, either on or around 21 June and 21 December in the UK and most of the northern hemisphere. (The winter solstice is the time when the apparent position of the Sun reaches its most southerly point against the background stars.)
Many people notice that the time of sunrise continues to get later after the winter solstice. The reason for this has to do with the slight variation in the length of 'natural' days throughout the year, which results from a combination of the elliptical shape of the Earth’s orbit around the Sun and the tilt of the rotation axis of the Earth. (The longest natural day is about 51 seconds longer than the shortest.)
However, for a clock to work, all days measured need to have a fixed, equal length. Each is therefore fixed at the average length of a natural day (this is where the ‘mean’ in Greenwich Mean Time comes from). By averaging out the length of each day like this, the clock time at which the sun reaches its highest point slowly drifts backwards and forwards as the months progress. There is a knock-on effect on the times of sunrise and sunset. The earliest sunrise occurs a number of days before the longest day and the latest a number of days after the shortest.
In London, the latest sunrise occurs about three minutes later than the sunrise on the shortest day.