Not SE, but SW, when I was 8 months pregnant we went to south Wales for a short break. we stayed in Mumbles which is on the coast, a lovely little village, very family friendly area.
Otherwise I would perhaps recommend Folkestone in Kent. Again, on the sea. The beaches are mostly pebbley but there is one sandy one and there are various play parks for children in the sea front area too. Broadstairs is another nice seaside town in Kent, with a big sandy beach and again very family friendly, we had some lovely days out there when we lived in the area.