I searching the data of the population + the income of the person in the post codes area for any digit layer in UK.
The most comprehensive dataset for Population and income is Census data however, the lowest Census geography is what is called an Output Area, which is an aggregation of postcodes with min. population and household size if 100 and 40 respectively. This minimum is set for statistical disclosure control (confidentiality preservation of individuals). So in your case, it will be difficult if not impossible to find official Population and Income data at postcode level