Sheffield Council's Socrata platform: https://data.sheffield.gov.uk/ (it's rubbish, let me know if you find anything useful)
I found "neighbourhoods" on data.sheffield.gov.uk https://data.sheffield.gov.uk/dataset/Neighbourhoods-Sheffield/wwma-jstu No idea what they're used for.
Deprivation Indices https://www.gov.uk/government/statistics/english-indices-of-deprivation-2015
Postcodes (for all UK) http://geoportal.statistics.gov.uk/datasets/ons-postcode-directory-latest-centroids User manual is here: http://geoportal.statistics.gov.uk/datasets?q=ONSPD%20User%20Guide%20(November%202017)&sort=name
Outlines for LSOA and other geographies from Census https://borders.ukdataservice.ac.uk//easy_download.html
and the UK government's Geoportal: http://geoportal.statistics.gov.uk/
MySociety's mapit project has boundaries for Sheffield and its various subdivisions. https://mapit.mysociety.org/area/2537.html Generally in WKT, KML, and GeoJSON formats.
A nice person on the internet has made lots of the boundaries available in other formats. Here are the LSOA for each Local Authority Districts in England: https://github.com/martinjc/UK-GeoJSON/tree/master/json/statistical/eng/lsoa_by_lad
Sheffield has GSS code E08000019.
Geoportal has boundaries all the Local Authority Districts (LAD) in the UK. Using this data, we can compute a latitude/longitude based bounding box for Sheffield:
Longitude: -1.802 to -1.324
Latitude: 53.304 to 53.504
(expanding the box to round the figures to 3 decimal places)
Much of the raw geographic data for the UK, such as the LSOA boundaries published by the census, are specified as coordinates on The National Grid (Ordnance Survey). In this system points are specified as a number of metres east, the easting, and a number of number north, the northing, of the National Grid's false origin. The false origin is Southwest of Scilly, meaning that all points in Great Britain have positive eastings and northings.
Sheffield is entirely within Great Britain, meaning that we do not have to deal with the added complication of using the Irish Grid system that is shared by Ireland and Northern Ireland.
Sheffield lies between 413km and 446km east of the false origin, and between 378km and 401km north. Thus generally eastings and northings for points in Sheffield will look like 4XXxxx for an easting and 3XXxxx for a northing.
Most web and other mapping systems use a latitude and longitude system based on WGS84 (World Geodetic System 1984) shared with GPS. This requires conversion.
I wrote a brief article on how to use pyproj to convert a bunch of coordinates.