Basically it's rubbish Penners
Britannia was one of the first parts of the Roman Empire to fall which explains why Roman law was late to come here (with the Plantagenets and the first crusades) and why our legal system owes more to the Saxons, Danes and Normans (who were always more Norse than French), especially for canon law (the church) which was the basis of our legal system before Henry II, when the crown began to overhaul the courts and keep the commonalty subjugated so the aristocracy could stay at the the top of the tree.
There used to more than 4 Inns of Court
which are basically where groups of barristers had their work places (chambers) and trained - they were run along the lines of universities or a posh guildhall.
Nothing much to do with Islam, but very much to do with land ownership and property law which is why the Lord Chancellor's job (think Cardinal Wolsey and Thomas Moore) was historically linked to the Treasury and how the monarch managed to keep some hold on the pursestrings until the 17th C
Historically I'd say the Inns had more in common with Judaism which was a lot more influential in western Europe economically into modern times - and of course Britain wasn't even looked on as being European for a large part of the last millennium so the Middle East wasn't terribly important until we went and got an Eastern Empire and certainly not in the time of the Knights Templar - Islam was the 'enemy' after all.