Sorry, OP, we've gone off on a massive tangent.
Re. your problem, I think the first step for you would be to get hold of the Judgement (if you're talking about a final hearing - there won't be one if you're not at that stage yet), as the Judgement helps you see exactly why the Judge found against you.
If in fact you haven't had a final hearing yet the all is not lost, but you need to focus on the cafcass report and if you feel that it is biased against you, you need to show the judge in what way, and why the cafcass report should therefore be disregarded (it would have to be exceptionally wrong, as I'm sure you realise, the court relies heavily on the cafcass report when reaching a decision).
You say that a "top London Solicitor" told you that Judges are down on custodial parents. The court want to see every child have contact with the father, so long as that is in the child's best interests.
I recently did a case where we had contact suspended for several years, after which it will be reviewed, but that was a very exceptional case of behaviour verging on physical abuse, and unless your ex's behaviour is similar extreme, you may have to accept that contact will (and should) take place.
Obviously you won't want to post details on this forum (and you mustn't, the proceedings are private), but it may be worth your while taking the most important papers you have (the court orders, Cafcass reports and statements) to another family lawyer for a second opinion. Ask them to be brutally honest about your chances and if they are pessimistic, then it may actually be better for your child to work with the court to let contact happen in a controlled and safe manner.
I don't know any of the details of the case, so forgive me if I've misread the situ.