That's not just a lack of investment.
OK, so they had a rubbish MIS system, OK so they didn't have a central case database, both fairly unforgivable, but to not be able to provide a list of cases that they are working on ?
Even without the help of IT systems it's possible to store this kind of information on something we like to call 'paper'.
Failure to do so suggests serious systemic management problems far beyond IT investment, as does the fact that the best quote they could get for a time recording system was £300,000.
Since integrated database, MIS and case management could have been provided by a couple of salaried in house codemonkeys, as is the case in many orgs, for not much more than the cost of a couple of salaries (throw in a few MS tool licences if you don't want go the FOSS route), I can definitely go with the failure to invest angle, but not doing this, or doing it badly is much more a project management and administration failure.
Good IT at this level doesn't require much investment, so just saying "you didn't spend enough money" is whitewashing over the same old endemic project management failures we keep seeing again and again in public sector organisations.
As is the case in many orgs that I look at, the IT failings are usually a symptom of crap management processes, not a cause. Of course, it costs money to have someone like me come and tell them that, and who wants to pay good money to be told that they're idiots ?