Public property

Roll-up, roll-up, roll-up for the biggest-ever government property fire sale!
Local authorities, the MOD, government departments - in trying to tackle the UK's debt mountain are all looking at what property they can offload. It's estimated that up to a quarter of public-owned properties could be sold off, mostly at auction, over the next two years.
Good news for anyone wanting to pick up cheap property for redevelopment, less good news perhaps for estate agents struggling to shift their existing property lists.
Here are some useful links:

MOD properties. Bit of an issue with this but I'll update the page as I find out more. Basically, property sales used to be handled by Defence Estates, who produced a basic list. Reorganisation put Defence Estates into the pan-departmental Defence Infrastructure Organisation (DIO) and it's got harder to find out what is, or is about to be, on the market. The most comprehensive source is the DOI disposals dataset on the site - here. Each list is available for preview or download and you need to look through them.
If you find a property you're interested in, you need to email the disposals team or the land management team for the area (or both!) - details on the pdf guide accessed from the DOI contact page here.

UK-wide auctions/repossession listings - Essential Information Group

Local authority property for sale. This varies from local authority. Some, like Cornwall Council, publish lists of property for sale online. However, with most you will have to contact that council's Estates Management team which is responsible for the disposal of land of property, including farms in rural areas.

Similarly, property for sale by utility companies may be listed on the company's own website, but most are put up for sale or auction through preferred estate agents (eg South West Water). You basically need to find the right links and keep checking. Here's the National Grid's property for sale list; here's Yorkshire Water's list, and here's the Coal Authority's list.

The Canal & River Trust (used to be British Waterways, relaunched 2012). The charity has its own property team who can give information and advice about empty waterside properties that may be available. The Trust's public notices page also includes information about moorings and some properties up for lease.

If woodland rather than waterside is more your thing, here's the list of Forestry Commission property for sale in Scotland, and in Wales. England is regionalised and you need to go through each Area Office.
Guidance on buying empty homes - The Empty Homes charity

The Society for the Protection of Ancient Buildings, publish a list for SPAB members of historic properties in need of repair and for sale or lease - SPAB property list

And, not exactly public property, but the Church of England publishes an online list of closed churches available for disposal - Closed churches and the Church of Scotland lists churches and other church property for sale on this website.