The PCR test is something that is easy to develop in any university and many NHS and biological labs. Because it relys on cycles of amplification and high sensitivity contamination and cross reaction with similar molecules have to be guarded for and the test thoroughly validated. But PCR tests are easier to develop than antibody tests and can be scaled up quickly. I am not quite sure what the government has by way of facilities to produce and scale up PCR testing, but it would have been up something like Public Health England to seek to get these facilities up and running and that would have meant that there would have been an executive, or even a political direction to do so.
I remember that in the early days of the pandemic some universities and research institutions in the US wanted to roll out testing but prevented from doing so by government. It really seems a political more than a logistic problem.
The same sort of obstruction seems to have happened with contact tracing. This is a well established way that is used for example to trace outbreaks of drug resistant TB or other infectious disease. This needs a local network of people trained to do so. I think we are currently not well placed to do contact tracing despite three months or more of notice. Again this is a political decision. When the government hides behind: ‘we are guided by the science’ they are really talking a lot of crap and is a code for avoiding blame for the very political decisions they have taken.