According to the Brighton Mortiquarian public health legislation enacted to curtail cholera and other epidemic diseases forbad burial in St Nicholas from around 1854, and this was followed in the 1870's by a clearance of monuments. This clearance must presumably have been rather selective, since in the early 1900's, as this postcard (postmarked 1906) shows, the churchyard was still well crammed.
The low stature of the trees in this picture also remind one that Brighton was originally a very treeless town (Trees in Brighton - an earlier opinion) and it was not until the later half of the 19th. century that tree-planting began in earnest. By the 1940's the tree-cover in the churchyard and along its boundary was quite extensive. Some trees and shrubs were removed during the second clearance in the 1950's leaving the churchyard more like it is today.
See also: "St Nicholas Churchyard".