TW
I need to preface my advice with a disclaimer, nothing on this board constitutes legal or financial advice - always consult a professional.
First of all, this is only an issue if you are receiving Income Related ESA in part or in whole. If you are only receiving Contribution Based ESA then it is not an issue as this is not affected by your savings and assets.
If you are receiving ESA(IR)
I cannot find any specific advice about this situation, there is something called a Junior Individual Savings Accounts (ISA), the Gov.uk site, which should not be treated as a definitive source of information states;
Parents or guardians with parental responsibility can open a Junior ISA and manage the account, but the money belongs to the child.
If this is accepted then the savings should have no effect on your ESA.
However, your moving your money to the ISA raises the issue of Deprivation of Capital and I cannot give you an answer on this issue, it is not just a question of your depriving yourself of the money there also needs to be an intent to maintain your benefit payments, so all I can suggest is that you get face to face advice from a trained and salaried advisor. Do an internet search for "welfare advice" with your postcode, town or county.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems