"If the UK government is prepared to make the resources available - maybe requisitioning private hire vans/drivers it can be done."

In theory yes but in practice it probably would not be that easy. The distribution centres are most likely already working near or at capacity. Not so easy to open up more distribution centres in a short space of time.

What would help is people trying to pool their orders. That would make a difference right away. I know that it is not that easy for everyone to do that but it is worth considering.