That doesn't really make sense. Any exemption would be due to government policy, so if service personnel are exempt the 'fight' has already been won? Your comment suggests that the government have made a policy which is not being adhered to.
I think you misunderstood my post. Allow me to clarify by expanding on it: Ahem:
Before the introduction of the poll tax, (by M.Thatcher and her team), the average service person living in barracks was not subject to 'rates' as the local tax was then called. Upon introduction of the said poll tax, service personnel had to pay as it was a tak 'on the head' rather than the property. As a consequence of this, service personnel living in barracks are still required to pay a local tax, now known as 'council tax'.
Still off-topic but on the Council Tax issue, it is perfectly true that service accommodation in England, Wales and Scotland is exempt from the council tax regime - as is service accommodation outwith the UK, of course.
The official line is that this allows a uniform rate to be charged irrespective of the local authority area. Whether fair or not, CILOCT is a legal charge in accordance with service terms and conditions. The MoD says that it pays to the local authorities an annual sum roughly equivalent to what it takes in in CILOCT within UK, in addition to which it provides some services directly which would otherwise be provided by the local authority.