What is the law in the UK on using corporal punishment on your own children?

There is no uniform law across the UK.

In English law, which also applies in Wales, the Children Act 2004 section 58 http://www.legislation.gov.uk/ukpga/2004/31/section/58 provides that corporal punishment is legal provided that it amounts to no more than common assault. ABH or GBH on a child cannot be "reasonable punishment" and are illegal.

In Scottish law, it is illegal to use corporal punishment on a child under 3, and for any older children, hitting them on the head or with an implement is illegal.

In Northern Irish law, it is merely illegal to hit a child on the head. The common law defence of "reasonable chastisement" remains available, as it used to be in England before 2004.