A child on licensed premises must be accompanied by an adult unless, say, the child has to pass through the bar area to get to the family's living accommodation. There is no specific 'supervision' requirement. The law applies equally to both the children of customers and those of the licensee.
Whether children are regarded as being 'accompanied' is open to interpretation by the licensing authority and the police. For example, if the licensee sits down for a meal with his children in the bar area, they're clearly 'accompanied'. However if he allows his children to play on the pool table in one bar, while he serves in another, it's quite likely that the authorities would then regard his children as being unaccompanied.
Section 145, Licensing Act 2003:
https://www.legislation.gov.uk/ukpga/2003/17/section/145