It is unfair of the company to flash civil service lower rates at you. If you were in the civil service 12 yrs, you would probably be on about 35K now, and all for short hours (9 to 5 with an hour for lunch). Also you would be guaranteed your increase every year and would not have to fight for it. Also most govt. jobs have plenty of back up & cover, so if you are out sick/holiday leave, the most urgent jobs will be done and you won't have to face a huge backlog when you return.
If you are only working the std 39 hour week, and are on that much money 35K, then you are on a good number. However, if you are prepared to put in more effort to further your career, you need to go to agencies & apply for more senior jobs. It is very hard to expect your present employers to give you a higher salary if you are doing similar work for the last 12 years. Are there any more higher level projects you could take on in your current job, to make you more 'valuable'? The way your company looks at it: they could take on a person with 2 or 3 yrs accounts experience, who would do your job for 22 or 23K. You need to add skills & make yourself more valuable.
I would try to move jobs if I were you. It is easier to secure a good pay increase by moving jobs. Also, when you work for the same company for years, they may take you for granted. They may think that you will never leave no matter what, and they probably feel they don't have to pay you top money to keep you from leaving.
HTH