We don't really have a historic environment law as such. I think the first question is by historic envirionment, do you simply mean archaeology or are you interested in protected historic buildings (listed buildings) as well?
I will name drop as many policies and legislation as I can, allowing you to google the policies you need from the web, if any of the other Bajr users spot a mistake please feel free to correct it.
I don't know anything about Ireland I am afraid, and some of these policies only apply to England.
Legislation
All legislation in England is national, passed by Parliament in Westminister. Scotland and Wales have their own federal style parliaments.
Specific legislation for archaeology is limited I can only think of the Ancient Monuments and Archaeological Areas Act 1979, although I think some medieval Treasure Trove Acts can be applied to metal detector finds.
The 1979 Act covers Scheduled Ancient Monuments (Protected Archaeological Monuments) and Archaeological Areas (covering urban archaeology in certain historic cities). The Archaeological Areas proved ineffective and although they still exist have been largely replaced by PPG16/PPS5.
Listed historic buildings are protected under the terms of the Planning (Listed Buildings and Conservation Areas Act) 1990. Conservation Areas, districts protected for their group value, fall mostly under the remit of planners.
English Heritage has been working for many years to replace these laws with a simplified unified consent regime under which both scheduled monuments and listed buildings would be protected as Heritage Assets, with the legislation being extended to protect Historic Parks and Gardens, Battlefields and Shipwrecks(?). These proposals were outlined in the 2007 Heritage White Paper and the 2008 Heritage Bill. Unfortunately the 2008 credit crunch, meant that Parliament was too busy saving the economy to discuss heritage and the bill was dropped before a law could be passed.
Planning Policy
Although the above mentioned laws are important, most of the archaeological work in England takes place under the terms of planning policy not legislation. Planning policy statements are published by central government and are 'material considerations', taken into account by local authorities when considering planning applications.
Up until March 2010 the Historic Envirionment was covered by two seperate policies;
PPG15 (Listed Buildings and Conservation Areas) and
PPG16 (Archaeology)
Although these policies no longer apply, I am attaching this link to PPG16, partly because it was so important to archaeology, but also because it is a really clearly written easily understandable document. PPG16 appears to be disappearing from the internet; this copy on the MoLAS website is the only copy I could find, so it may soon disapear into the ether.
http://www.museumoflondon.org.uk/NR/rdon...507144.pdf
In March 2010 PPG's 15 and 16 were replaced by PPS5: Planning and the Historic Environment, covering listed buildings, conservation areas, registered historic parks and gardens, designated battlefields and I think shipwrecks. I mention these by name because the committee who wrote it refer to 'heritage assets', but from memory do not explain what this encompasses. PPS5 cannot be read on its own, English Heritage's accompanying Practice Guide needs to be read with it.
PPS5 also refers to the 'Government's Statement on the Historic Environment for England 2010' although I don't know much about this.
The Government has recently changed and it is possible that some of these policies could be altered or amended.
I hope this helps