Christian yes - C of E no it wasn't (don't think so anyway). Certainly in recent years it hasn't been, and the Service Chaplains have been chosen to be "one of each", ie CofE, RC and CFSC. I remember an old mate - Fr Tom Devaney - leading it once not too long ago.
Also don't think there are any non-Christian Service Padres.....but, as ever, I stand to be corrected on both counts.
As to recognition of other faiths, there are moving pictures on the big Remembrance thread of Stars of David and Crescents in the Field of Remembrance.