If you wish to object you should send an email to planning@lewisham.gov.uk quoting the reference DC/10/74983 and stating the reasons for your objections.
Does anybody know if the tree(s) have a TPO?
This would appear to count as 'infill' development and therefore it is worth quoting council policies:
HSG 8 Backland and In-fill Development
Backland and in-fill development will be permitted provided the following criteria are met:
(a) sufficient garden depth and area should be retained by existing dwellings (see Policy HSG 7);
(b) the scheme must respect the character of the area, including the cumulative impact;
(e) on a road where additional on-street parking would not be permitted the development would not worsen any (on-street) parking problems;
(e) there should be no appreciable loss of privacy and amenity for adjoining houses and their back gardens;