i can recommend a fantastic piano teacher but she doesn't do home visits. Jane Sebba who does lessons in Hornsey Rise Gardens (on the 41 bus route) . let me know if you want more details. She teaches piano, accordion, bassoon and recorder. I'm learning accordion with her (not having played the piano beforehand) and can attest to her fantasticness.
Just wondering whether you're still looking for a piano tutor for you and your family? I am a Harringay based music tutor with 2 years experience in teaching! I currently teach two other families, one in the local area and one in Highbury and Islington. The way the pricing works is that normally for half an hour it costs £20, however when I teach a group of 3, the price drops to £15 for half an hour. If the three of you are all beginners, I would recommend that you take half an hour lessons each to begin with. If this interests you, I'd love to schedule a time when I could come round to meet you guys and I'd give you a trial lesson for free to see if you like the way I teach etc.
My number is 07402692696 :)