You can apply for any school in the country, but you're unlikely to get a place at an oversubscribed Kent school if you live in Somerset or at an oversubscribed RC school 15 miles away if you're not Roman Catholic, so you need to be realistic.
Look at local authority websites for any areas you'd consider - info on eligibility criteria, furthest distance of admitted pupils etc should all be there.
As for the area you're talking about, there were a number of good schools there years ago but schools can and do change rapidly - I wouldn't form an opinion of one until I was close to applying, basically.
We are considering of moving to Greenwich, & one of the main reasons for moving there is the Brooklands Primary School. This school has very high ratings, at least on paper. 1. Any first-hand experience? Does anyone know of someone whose kids go to this school? Whats their view? 2. Are there any good secondary schools in this area - what are the good options after year 6? 3. Can people from Greenwich council apply to the grammar schools in Bromley?