Well, the GOV.UK code (https://www.github.com/alphagov) is your 80% (or more likely higher) solution. It's based around many micro-services that integrate over HTTP, so it's extremely extensible.

However, even with the software being perfect, you still have very high barriers of entry to overcome: 1) the local authority is likely to be locked into a 5- or 10-year contract with its current supplier 2) the choice of supplier is rarely (if ever) based on technical excellence/licensing strategy. Usually the people commissioning the IT don't tend to have a very deep understanding of technology, licensing, etc