There are a number of key legal instruments that govern heritage protection in the UK. These form the foundation for all other legislation governing heritage, whether in conflict or natural disasters.
England: they are summarised here by Historic England in their Heritage Protection Guide
Scotland: they are summarised on Historic Scotland’s page: Scotland’s Historic Environment Policy
Wales: Managed by CADW. Although also subject to many of the same instruments as England, Wales has also passed the Historic Environment (Wales) Bill on 9 February 2016.
Northern Ireland: Formerly managed by the Historic Environment Division of the Department of Environment, “From May 2016, nine new NICS Departments are being established and the functions of the Department of the Environment will transfer to three of these new Departments. The Historic Environment Division will be moving to the Department for Communities.”
There is currently no single repository for legal information, but the website is currently available here.