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I have a bunch of locations in a google fusion table, I've also got a population density spreadsheet from The Guardian so I have some data on population density.

But I was wondering if there was a data set that would give me the locations (postcodes, whatever) that were within 30 miles of, say, 100,000 people in the UK?

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From this Q&A at GIS SE (Worldwide population density data not grouped by country) (updated by me to reflect link changes):

One of the best gridded data sets is CIESIN's Gridded Population.

See Gridded Population of the World (GPW), v3 for more details. The best resolution is 30 Arc seconds (The global data set has resolution of 2.5 arc minutes - Deer Hunter).

To find the places, have a look at this question at GIS SE: Algorithm for finding population for a given center point and radius in US

In general, I would advise looking for geospatial data at GIS Stack Exchange before going here. The chances are quite high the question has already been asked and answered there.

EDIT: through gracious assistance of ldodds, UK-specific reverse geocoding facility (at Ordnance Survey) has been identified:

http://beta.data.ordnancesurvey.co.uk/datasets/os-linked-data/explorer/search

with documentation available at http://beta.data.ordnancesurvey.co.uk/docs/search. This would be the last stage in the processing pipeline.

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    You could also look at combining this with some data from the Ordnance Survey. For example, if you find the lat/long of populations of 100,000 people using the data that Deer Hunter suggest, you could then relate this back to UK locations, including places, post-codes, etc using the search API on the beta OS Linked Data site: beta.data.ordnancesurvey.co.uk/datasets/os-linked-data/explorer/…. Docs, including notes on geo search, are here: beta.data.ordnancesurvey.co.uk/docs/search
    – ldodds
    May 24, 2013 at 15:18
  • @ldodds - thanks, this qualifies as an answer, since I provided only worldwide data. OS data are somewhat more detailed.
    – Deer Hunter
    May 24, 2013 at 15:23
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    Its not a complete answer though as the OS data doesn't have the population data, seems like a mixture of the data sources would work. Feel free to revise your answer to include it :)
    – ldodds
    May 24, 2013 at 15:36

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