I think it might well be related to the Ampleforth College Fire Squad who were uniformed according to this article.
It could well be a fire hat badge for the school. SL = Section leader perhaps. or perhaps it's scout related?
The resemblance to Ampleforth's CCF and OTC badges is a strong one but it is not her OTC, JTC or CCF badge.
http://www.ampleforthjournal.org/V_109.pdf