@mummywhatyoudoing To be honest, if you are not in last year’s catchment circle for Meridian / Halstow, then you really do need to consider other options. You need to look at ALL of the schools near you, on the online catchment map to see which ones you might be in the the circle for. Otherwise, if you don’t have the local ones on your application that you will definitely get in to (ie do millennium or invicta catchments come out as far as you, or any others?), as even your last priority place (no 5 choice on the form), then you may not get a place at any of your choices, and may get an undersubscribed school, that you didn’t put on your list, that still has places, at the edge of the borough, maybe two bus journeys away.
So visit all the Local schools, do the research (re the catchments), and make sure you put down one that you are pretty much guaranteed a place at, even if it is your last choice. Make sure you rank your schools in true order of preference - so put your favourite first, second-favourite next, etc but you do need to be realistic about choice number 5. Better to have a local school, even if not one of your favourite choices, than one miles away, which you really wouldn’t have chosen, but have just been assigned.
The other thing I would say about primary schools in Greenwich is that there is usually a lot of movement throughout all 7 years - lots of people moving due to jobs etc, so there may well be spaces becoming available (if you are on the waiting list) after school starts in September. At my dc’s primary, there were people moving away every year. So all is not lost, on the 1st September, if your dc does not have a place in your top choice school, and if you stay on the waiting list.
edited to add - I got distracted by one of my teenagers while writing this post, and have just spotted that @Toomanyminifigs beat me too it, and I have just repeated a lot of what is in their post, sorry!!