I know that Grif has just gone through the whole process as a British guy; however, as you are a Polish citizen now, I think the rules regarding British people will not apply to you as the Polish authorities will regard you as Polish first and British second.
It's a difficult one, I would like advise you to go to the Polish consulate London, but whatever you do for god's sake check their advice that they give you, as I have heard of them giving out the wrong advice to People.
I don't think you need anything to prove that.
I am afraid you have to krysia, Polish people can just get the form from their local authority office, but if you live in Poland you have to go to the Embassy in Warsaw and pay, I think Grif was telling me it was 600zl but it is cheaper in the UK.