Rainbowinthesky - you are probably not going to get particularly useful answers without giving more information about your life/income/expenditures.
I can understand why you wouldn't want to do that here because it does open the door for people to make comments (and believe me, they will!). But without more detail, I don't think you'll get a real answer here.
I'll pull a number out of the air and start by saying I think you'd need at least £1000 per month (after taxes) over and above mortgage, petrol, food, household bills. That money will go toward pension contribution/savings, holidays, birthdays (and gifts at birthday parties), Christmas, one-off expenditures (replacement of fridge, boiler/car repair, etc), hobbies, meals out, clothes, etc.
You are not clear about whether you are including school fees in your expense list in the OP, or whether you are asking if 'minimum' per month is expected to pay for school fees (among other things).
If your budget is very tight, is it possible/likely your family would qualify for a bursary or scholarship?