The Ministry of Defence was heavily involved in the logistics planning and execution for the mobile testing units across England and Wales.

Yes the British MOD has a record of being very good at logistics [1]

"One country that has achieved an unparalleled level of efficiency and responsiveness in its logistics and sustainment activities is the United Kingdom (UK). The British Ministry of Defense (MOD) has wholeheartedly embraced outsourcing many of these functions to the private sector."

Also of interest: "One of the primary reasons why the MOD is willing and able to enter into long-term PBL-based service and support contracts with private companies, not just British firms but global providers, is because of its attitude towards the private sector. The MOD views the private sector as a positive contributor to their mission. It works hard to establish a collaborative relationship. MOD officials are demanding and insist on adherence to contracting requirements. But they treat the private companies as partners, not adversaries."

[1] https://nationalinterest.org/blog/the-buzz/britains-innovati...

I had the good fortune of first-hand experience of working with the MoD for a small slice of the mobile testing unit logistics, and would absolutely echo the sentiments expressed in that blurb.

The whole article is a fascinating read, especially when I noticed that it was written in 2016 :-O

The MOD has been heavily involved in logistics from the start; they were the ones delivering the PPE to the NHS stockpiles (my understanding is that the biggest hospital in the region acts as storage and a distribution centre for the smaller, more rural hospitals that don't have storage space). They weren't involved with taking PPE from those local distribution centres to the actual hospitals, however, that was up to the NHS to do what they had always done, and for some areas this was the bottleneck where shipments slowed or were even lost.