That's the Irish Sea sorted. What about the North Sea?
Actually the Continental Shelf Act 1964 and the Continental Shelf (Jurisdiction) Order 1968 (which define Scottish waters in the North Sea as everything above the 55th parallel) are out of date. They do, however, represent the "traditional" boundary between England and Scotland.
What you need to look at is the Scottish Adjacent Waters Boundaries Order 1999. This defines the Anglo-Scotland boundary in the North Sea on the principle of equidistance. As a result the boundary runs North-East from the coast at 55° 48' 42"N 02° 01' 54"W to 56° 27' 10'N 00° 38' 41'W where the boundary heads East to 56° 36' 31'N 02° 36' 26'E.
Thankfully the Department of Energy and Climate Change have a handy wallchart that shows the boundary. It also shows all the offshore oil and gas infrastructure in British waters. It demonstrates that the SAWBO puts a relatively small part of the Central North Sea into English waters (compared to the old 55th parallel boundary). It does not however, affect the remaining Scottish parts of the Central North Sea, the Northern North Sea and West of Shetland where most of the oil lies.
There is absolutely no case for any line further north than the one defined in the SAWBO nor any line further south than the 55th parallel - all in accordance with UNCLOS.