There are lots of things you need to consider:
if you move in together then (and I am assuming as you say you work part time) then your benefits will most likely stop as his income will be taken into account. This will mean that your 'income' will drop. Will you still be able to affords your half of the bills and standard of living?
Will you be pooling all of your income and splitting everything equally? or will you both keep your income and then split the bills 50/50? if so be mindful of the above point regarding your benefits.
Where will you live? do either/both of you own your house? if so will you be selling and buying jointly? if moving into 1 then will you be contirbuting towards the mortgage or have a stake in the house? will either of you be giving up a secure council tenancy? if you split then it is unlikely you will get another one.
Will there be enough bedrooms for all the kids?
What is the price of private school? you are looking at 15k plus all the extras - trips, meals, uniform etc, none of which come cheap!!
How about other inqualities between his and your kids - will he be spending thousands at xmas and birthday compared to you spending £100s?
Do either of you have debt?
a year when you both have kids is not a long time, i would adivse caution and leave it a few more years before moving intogether. if the worst happens and you split you may ahdv put yourself and your children into a vunerable position.