Agree with Andrew about using chemicals to strip the rust. Far easier and less likely to damage the good parts. Here in the states this Evaporust is very popular.
Thompsons Ltd | Evaporust Evapo-Rust Remover 5L Safe Rust Remove Metal Treatment This is just the first UK site that popped up so shop around for better prices and you may only need a 1 liter size for the parts you mentioned. You may need to do some scrubbing with a stiff brush occasionally during the soaking period if the rust is stubborn. Won't harm paint, plastics or rubber. Doesn't leave any rust protective coating so replacing some of the screws may be a good idea.