Martin, this Child Support proceeding should've never be filed and judged by a Family Court (which is a State Court). It's attribution of the Federal Justice to decide in Child Support proceedings where defendant lives in another country. It should be judged by the Federal Court in the capital of São Paulo.
There's a International Convention of the UN (known as "New York Convention") about child support, published in Brasil as Decreto n. 56.826/65, and also the Law n. 5.478/68, art. 26, which says the Federal Justice attribution.
Ask your lawyer if he is aware of the above rules.
But, if the Federal Court issues a non favourable decision, saying you should pay, it will send a request, under the terms of International Treaty, to the UK's Court to demand you the payment of the child support, which is something the State Court can not do.