This situation is awful and you have my fullest sympathy.

However, as far as giving advice is concerned… unless there is proof that you are not the child’s father, then regardless, you will be liable for child maintenance and the agency will pursue.

Quite obviously from your post, the agency have calculated liability.
Has this been achieved by actual information provided to the agency OR have they applied a penalty OR default maintenance decision?
If the latter, this can be altered to a proper maintenance calculation and may well decrease the alleged arrears amount.

You need to give this matter your attention, it will not go away.

http://www.afairercsaforall.co.uk