Once Belgians call UK to help, they defacto temporarily surrender their sovereignty to London. That gives Grey field of manoeuvrer.
UK sends BEF to Belgium as peacekeeping force, and then "demands" from French to give up what French never wanted, such as "forcing them" to stay south of Meuse, but simultaneously guarantee French unobstructed passage through Wallonia south of Meuse.
Belgium: "UK, why you didn't kick out French out of Belgium?!"
UK: "Its called tactful diplomacy and compromise, you Ardennian barbarians. You're the ones who called us for help, so don't question the means by which we provide it."
And if Germans accidentally, for example during counter-attack against French violate Belgian territory, UK has its CB to declare war on Germany, for "escalating already inflamed situation in Belgium".