Whereabouts in Southfields are you? My son goes to the playroom on Garratt Lane (
http://www.theplay-room.co.uk) and absolutely loves it there. It is a small nursery so he gets lots of attention. They may have availability, or i know the lady who owns Jenniflowers in Southfields (
http://www.jenniflowers.co.uk) and she is a lovely lady. Hope you find someone you love for your daughter NS good luck with the move!