zonoma, while being vectored I think it's sufficient if the first controller gives his/her restriction. The second restriction we can take with next controller. An example, you're coming from the North Sea and cleared direct LOGAN for the LAM3A arrival. Before LOGAN you're told to fly heading 265 I would expect the inclusion of 'level abeam LOGAN' if you want us there. If you're done vectoring and clear us, for example, direct SABER a join the arrival would tell me that STAR restrictions now apply again. But I rarely hear that term in the UK? If you just clear us direct SABER or keep us on a heading then the next controller will have to restate the next level restrictions. Overall London works very well but I do hold on to the principle that a heading instruction nullifies any previously given arrival. Now I also know after experience (and after this thread) that the level restrictions are important so I kind of plan for them even though the terminology hasn't made it clear.
MATS Pt1 is not a document familiar to most pilots I am afraid. Is it a case where they use an SID as an example, as someone suggested?