How to group data and construct a new column - python pandas?

Use groupby ngroup to "[n]umber each group from 0 to the number of groups - 1":

df['unique_id'] = df.groupby(['postcode', 'house_number']).ngroup()

df:

   postcode  house_number  col2  col3  unique_id
0       111           222     1     5          0
1       111           222     2     6          0
2       111           444     3     7          1
3       333           333     4     8          2

insert can be used to make it the first column if needed:

df.insert(0, 'unique_id', df.groupby(['postcode', 'house_number']).ngroup())

df:

   unique_id  postcode  house_number  col2  col3
0          0       111           222     1     5
1          0       111           222     2     6
2          1       111           444     3     7
3          2       333           333     4     8

*Note: sort=False can be used to ensure that groups are enumerated in the order in which they appear in the DataFrame:

df['unique_id'] = df.groupby(['postcode', 'house_number'], sort=False).ngroup()

Or

df.insert(0, 'unique_id',
          df.groupby(['postcode', 'house_number'], sort=False).ngroup())

Otherwise groups will be enumerated in the "order in which the groups would be seen when iterating over the groupby object, not the order they are first observed."

DataFrame and imports:

import pandas as pd

df = pd.DataFrame({
    'postcode': [111, 111, 111, 333],
    'house_number': [222, 222, 444, 333],
    'col2': [1, 2, 3, 4],
    'col3': [5, 6, 7, 8],
})