What's that children's book..

[seeker]

...where a child plays with a family of children from next door who turn out to be ghosts?

Green Knowe by L M Boston?

Although that's children who lived in the same house in the past.

The Amazing Mr Blunden by Antonia something?

Tom's Midnighy Garden?

Moondial?

Scrap that, as I've just remembered that you said "lived next door".

'The Children Next Door' by Jean Ure?