Lewisham council has a section on 'Animal Fouling and dead animals' under its Environment/street cleaning site. It says:

Dead animals

If you discover a dead animal in a public area or street, phone us on 020 8314 7171 and we will remove it. We also remove dead animals from the gardens of private residences.

'course it may not be possible to contact anyone at weekends but they do collect, as they did for us with a dead fox last year.