Ok, so the best source of information I've found so far is this report from the NAO:
The general story is one of a very large, centralised operation being set up at the outset. There is this commentary in that report:
Rightly or wrongly they seem to have believed that it was more feasible to build up central capacity rapidly, than it was to build on existing local capacity rapidly.
The longer term picture sems fairly clear - it was recognised that local knowledge/capacity needed to be used more, and that was reflected in changes in the way the system worked throughout 2020, with the number of call handlers being employed by the national service being reduced by around a third in the autumn.
There's this table which shows the change in numbers over the course of May-October:
View attachment 252572
That table doesn't seem to include contact tracers employed by local authorities - who as far as I can make out, are now handling a greater proportion of the work. So it's hard to see how the numbers compare. The national service still operates with quite a large number of people though.
A lot of this argument seems to be about the wisdom of setting up a central "national" system rather than building up at a local level. The change in approach since the initial stages seems to confirm that the initial idea was indeed over-centralised. The report looks at what other countries have done, and comments that most of them did not try to do this.
My question is whether it's the "outsourcing" as such that was the strategic error, or was it the excessively centralised approach.
That's why I would like to understand what it would have looked like, if the initial approach had been much more focused on local contact tracing operations. Given the seemingly very large number of extra people that would suddenly be required, would that have had to involve some form of "outsourcing" too? The government appears to have decided that this rapid expansion at a local level was not feasible and of course they might have been wrong.
To me it looks like the situation with the vaccine rollout is rather different because effectively there's been nearly a year to prepare for it, and mass vaccination is something that happens in any normal year. The contact tracing operation involved recruiting 18,000 people only a couple of months after the start of the pandemic.