There is no way that pressure can be applied to an individual to not voice their concerns via a petition. As long as you do not use your rank or in-Service status and sign it as Mr/Mrs/Miss/Ms then there is absolutely no issue at all. It is a basic right of every citizen (civilian or military) to be able to voice their opinion in the UK - it's just that those of us who wear HM's uniform must not overtly criticise the Govt whilst wearing said uniform or acting in a Service capacity. Whilst off duty, in the comfort of one's own home, the same individual is able to voice personal opinions as much as they like (like signing a petition).
Think about it, if you were not able to voice a personal political preference then you wouldn't be able to vote!
Facebook is subtly different as many persons put pictures of themsleves in Viggis/Vikings - then if you criticise then their is the faintest argument that you are bending the rules. But for a petition there is no such danger as long as no reference is made of your status (ie. Rank or connection to the Service)
CPL Clott