You're talking about your money- not theirs- right? They don't know it's there.
Why do you feel that your child(ren) have a right to a savings pot?
Are you actually reading the advice which is about saving for your own essentials before your child's 'pot'?
Why are you getting yourselves into a financial mess by putting money into savings for them, above saving for your own essential outgoings?
As PPs have said- the outgoings now of over £2K are predictable to an extent.
Glasses, uniforms, car repairs etc.
This is what you should be saving for- not s nest egg for your child.
Boiler and leaks- do you have Home and Contents insurance? Can you claim, minus the excess?
You need to take a big step back and take the emotion out of your money-choices.
If you had loads of excess cash each month, fair enough, earmark some of it for your kids in the future. But you don't.
To give a comparison, when I left uni in the late 1970s, I had a savings pot of almost £3K. Nothing from my parents who were poor. I'd got a full grant then, not spent it all, and worked during all my holidays. I bought a car as a student (ok it was a rusty old banger.)
Because I had to do it all myself, and not get a penny from my parents, it taught me to save and budget.
Even when my DCs were learning to drive we bought them a car to share, but they paid towards the insurance.
We have been able to give them a very big chunk of money towards their own homes.
You need to manage your own money first and foremost before putting it aside for a child you doesn't even know it's there.