In any case, my sister used to work in an MP's office and even when you get auto replies they tally it, and weight it quite heavily as a representation of constituents' views (unless it's a template letter in which case it goes straight in the bin).
It definitely has more effect than signing a petition - most of them are super dumb (lower taxes!) and as far as I know not a single one has actually changed the government's position. It's just too easy to sign them and too many dumb people do it.