Because it's in the script for them to go to the laundrette. Just like it's in the script that they must eat in the cafe, buy clothes, fruit/veg etc from the stalls and drink in the pub every night.
Must admit it's always annoyed me that they don't have their own washing machines, think of the money they could have all saved over the years if they'd bought their own.
I don't even watch Eastenders anymore btw.