I don't have any legal knowledge so please don't take this as gospel but from what I know, the child is placed with the mother when they are young, unless there is a good reason why they should live with their father (and this has to be serious ie drug habit, prison etc)
And for your child to live with you... means more than 50% of the time. A child needs a home, not to be shipped between two places. I really doubt any court would allow that, or any solicitor would suggest it. Just tell him you can get legal aid and if that's what he's been told you are more than happy to fight him. I expect it's all rubbish.