Hi Hazlenut,
If you have Ellen's maiden name from the census you could look through the BMD indexes. After 1911/1912 the mother's maiden name is given so you may have a chance of finding some descendants. It's a bit of a gap from 1901 - 1912, you would either have to buy likely birth certificates stating the expected father or mother's maiden name, or perhaps you could try the parish registers (available from LDS if you are not local, or maybe still at the church) to see if there were any baptisms.
Another option would be to try the electoral roll to see if you can find where John & Ellen were living. You can access recent electoral rolls for free at
http://www.b4usearch.com/ but this won't help unless you can find some of the children's names - you could write to all the Price families in the Birkenhead area, but with such a common surname it would be a thankless task I suspect! It's always difficult looking for descendants from this time period - have you tried GenesReunited, you never know, someone else may be researching the same family.
Sorry there is no easy answer to this,
Jean
