I can only say that in British English you can not say
How much do I pay?
Well of course you can say it but it would be grammatically incorrect if you were asking the question of how much you needed to pay for something.
You could say
Many people do and it's very slightly inpolite / abrupt.
It probably is the closest to 'Ile płacę?'
Otherwise it would have to be
How much will it be? Or How much will it cost? Or How much do I need to pay?
You can only use 'how much' + uncountable noun / singular or plural noun or with the verb cost or be.
'How much do I pay' would only make sense in the context of asking someone how much you routinely paid for something in the past. Eg. In the context of monthly payments for electricity. (How much do I pay [every month for electricity])