Hi OP
So the area that meridian is in, is a good area.
You should be able to find old style Victorian houses for rent or you head to the river more there are new build. You probably want to stay on the same side of meridian school if that makes sense? So don't look across the other side of Trafalgar road unless you can find something in park row.
Meridian is a good friendly school. It's grounds are often used as a music school for trinity on weekends. It is a short walk to the maritime museum, cutty sark, river and Greenwich market and central greenwich.
Otherwise you may want to try more Westcombe Park way of town or even Greenwich peninsula.
In terms of poshest areas in Blackheath, you are talking about the Cator estate. Go for a walk around the Cator estate and you will see what I mean.
Also West Greenwich is posh and has some big houses.
But east greenwich (smaller houses) is still a good place to live. Just mind that you are not too close to a busy road and check pollution levels.
Old wooolich road would be a good road to look for a rental to get into Meridian.
Good community and generally safe.