No, if you are claiming childcare costs as part of your Social Work Bursary, you wouldn't be able to also claim through HMRC Working Tax Credits, Universal Credit or another publicly funded body. You can only claim from one agency so you would need to decide between claiming from HMRC, Universal Credit or from us.
For example, if you're claiming the childcare element of Working Tax Credit for one child only and try to claim the Childcare Allowance from us for a different child or to top up your childcare payments, you will not qualify for any Childcare Allowance payments from us.