You asked

I am looking for information on the population density and average disposable income in certain areas of London, broken down by postcode.

The post codes I am interested in are;

E1, E2, E3, E14, SE1, SE16, and N1

We said

Thank you for your request. The requested information is not held by the Office for National Statistics (ONS).

Population density by individual postcode is not available. Population density is available by postcode sector. If this information is of interest, please contact the Census Customer Services team - census.customerservices@ons.gov.uk

ONS do not have any statistics on disposable income at postcode level. Model-based estimates of household income are available at middle super output area (MSOA) and are available here http://www.ons.gov.uk/employmentandlabourmarket/peopleinwork/earningsandworkinghours/bulletins/smallareamodelbasedincomeestimates/2015-10-20. These are the most geographically granular official statistics on income that are currently available.