When we first meet the doctor, he's on earth because his granddaughter Susan is at school in London - the first companions, Ian and Barbara were her school teachers, who got curious about why she apparently lived in a junk yard and ended up being kidnapped by the doctor to preserve his identity.
The relationship has never been explicitly explained, but Susan always called the doctor 'Grandfather'
Of course, it could also be that Rose wasn't quite telling the truth when she said it was her mum who was pregnant - there's quite a lot of fan fiction based on that idea!