Central London reference, open views decide
Times are computed for the central London reference near Charing Cross, 51.51° N, 0.13° W, with a flat horizon. Greater London's spread changes moonrise by only a minute or two; your horizon changes it far more. Hilltops such as Primrose Hill, Parliament Hill and Greenwich Park give the open eastern view needed to catch the Moon soon after it rises.
Source: GeoNames — London