In case you want to save to parquet it's pretty easy

Parquet

import dask.dataframe as dd
import pandas as pd
import os 

fldr = 'data_pq'
data.to_parquet(fldr, partition_on="PostCode")

this save data for every postcode inside a folder called PostCode=xxxxxxx which cointains as many file as the number of partitions of your dask.dataframe.

CSV

Here I suggest you to use a custom function write_file.

import dask.dataframe as dd
import pandas as pd
import os 

fldr = "data_csv"
os.makedirs(fldr, exist_ok=True)


def write_file(grp):
    pc = grp["PostCode"].unique()[0]
    grp.to_csv(f"{fldr}/{pc}.csv",
               header=False,
               index=False)
    return None


data.groupby("PostCode")\
    .apply(write_file, meta=('x', 'f8'))\
    .compute()

# the same function works for pandas df too
# data.groupby("PostCode").apply(write_file)

You should check how it works performancewise and eventually play with scheduler.