I'm not sure how rigidly this is enforced, but....
It is illegal under the Foreign Enlistment Act 1870 (c.90) for a British Citizen to serve in the armed forces of another country because:
“If any person, without the license of Her Majesty, being a British subject, within or without Her Majesty’s dominions, accepts or agrees to accept any commission or engagement in the military or naval service of any foreign state at war with any foreign state at peace with Her Majesty, and in this Act referred to as a friendly state, or whether a British subject or not within Her Majesty’s dominions, induces any other person to accept or agree to accept any commission or engagement in the military or naval service of any such foreign state as aforesaid,— He shall be guilty of an offence against this Act, and shall be punishable by fine and imprisonment, or either of such punishments, at the discretion of the court before which the offender is convicted; . . . - See more at:
http://windowintopalestine.blogspot.co.uk/2009/02/british-jews-serving-in-idf-israeli.html#sthash.g1lDw2jZ.dpuf