As well as supporting our Lewisham neighbours in any event, this is important to Greenwich borough residents too. Queen Elizabeth Hospital in Woolwich, the alternative posed, is very far for many ill or pregnant Lewisham residents. QE Hospital would become very pressurised for all users, even more than it already is.
More on the Save Lewisham Hospital website.
Interesting list of people born in Lewisham Hospital on the Transpontine blog.