Social Services are wrong. Mediation is not appropriate in cases where there has been domestic abuse, and you did not need to do mediation, you could have applied straight to court, which is what I would suggest you do now. The court will be able to make an order that has to be stuck to - mediation is just an agreement between you and the father, it cannot be enforced. A court order can be enforced.
As you have been subjected to domestic abuse you may well be eligible for legal aid - check here: www.gov.uk/check-legal-aid
You can do so on form C100, cost is £215, unless you are on a low income/benefits, in which case you may be eligible for fee remission and should complete form EX160. I have included the relevant links below:
C100 form: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/946762/c100-eng.pdf
EX160 form: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/952045/ex160-eng.pdf
E160A Notes: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/958038/ex160a-eng.pdf