In Kent there are a variety of schools that offer a limited number of OOC places but these are usually by a very high score so if you are not looking for the superselective variety you may not find an option that works with the distance you are away from any Kent pass school.
The new Weald annexe of TWGSB is a new phenomena. The girl's equivalent, Weald of Kent annexe near Sevenoaks came out all the way to Orpington and Petts Wood in recent years but I haven't heard that it made it to Greenwich and don't know what the boys one has been like in its first year for distance. Both of these annexes like their parent school just require a pass. Most of the 'pass' ones are on Parish or distance or a combination of both.
It is possible to take the test as an OOC student and then if your child passes move into the parish of the school you are most keen to attend in Kent by around first week of December, but that leaves you with two terms of primary school to grapple with so creates its own challenge.
There are other grammars in other areas that also have no catchment, but nearly all are superselective, see this thread
viewtopic.php?f=5&t=57820If you are looking to move why not move into the catchment of a good comprehensive and then no 11+ stress?