You asked

Please provide me with any information regarding the ages of the inhabitants of a particular postcode in Brecon, Powys?

We said

Thank you for your email requesting data pertaining to the ages of the inhabitants of a particular postcode in Brecon, Powys.

The Office for National Statistics (ONS) are not able to supply these data at this level of geography (postcode), however, the following information may be of interest to you:

Please note that, in the following tables, in order to protect against disclosure of personal information, records have been swapped between different geographic areas. Some counts will be affected, particularly small counts at the lowest geographies.

Postcode Headcounts and Household Estimates - 2011 Census, are available at:
http://www.nomisweb.co.uk/census/2011/postcode_headcounts_and_household_estimates
This release contains summary results - 2011 Census estimates of usual residents broken down by sex and an estimate of the number of households with one or more usual residents - for unit postcodes in England and Wales. In addition to this, a separate table detailing the postcode/OA splits is provided.

Age by single year data are available for postcode sectors:
http://www.nomisweb.co.uk/census/2011/qs103ew
You can use the "Query data" option to refine your search to various geographies. For example you might select postcode sector (some) - then select 'LD3 0'. Clicking on the small map icon next to each sector will show you the outline you have chosen on a map. You can also refine your search to select all Age categories.

The same table is available at Output Area (low level geography).
Use the "Query data" option to refine your search to the geography: 2011 Output Areas (Some). Now: List areas within Powys. Clicking on the small map icon next to each Output Area will show you the outline you have chosen on a map and allow you to identify its location.

ONS Geography provide a lookup (output_areas_(2011)_to_enumeration_postcode_sectors_(2011)_E+W_lookup) between 2011 Output Areas and postcode sectors: https://geoportal.statistics.gov.uk/geoportal/catalog/content/filelist.page?&search=postcode&cat=LU

If you have any further questions may I suggest that, rather than using the Freedom of Information route, you contact Census Customer Services directly. They will be glad to deal with any census related queries and the process is much speedier.
Web: https://www.ons.gov.uk/census/censuscustomerservices
Email: census.customerservices@ons.gov.uk
Tel: +44 (0)1329 444972
Census Customer Services: ONS, Titchfield, Fareham, Hants, PO15 5RR