I think the difference in stance has nothing to do with the leadership but rather the consideration of the science as presented and an appreciation of timescale. This isn't over in 12 weeks, we might have control of it by then, i.e. turned the tide. This is here until we have a vaccine, an effective treatment and some measure of herd immunity. Until then we are very much balancing supply and demand of health system and that includes most importantly health workers. Hence not closing schools completely but turning them into daycare for health workers children and as a by product those others who will benefit from being cared for.
A quick look at the UK news re. supermarkets and social distancing from the outside and comparing it to behaviour in some(but not all) other countries can only lead to the conclusion that the UK population in general (but not all) will not be able to adjust well to 3 months behind closed doors followed by another three when the second wave starts.
If the UK population were all automatons then full lockdown on day 1 would be viable. They are not thank god, they are liberal and free thinking and experimental and adventurous. That's why they lead the world in so many fields from the arts to science to social justice. These are the benefits of the UK. But with those benefits come disadvantages. It's a balancing act and despite the general tone on bluemoon, the latest polls show that the majority of the UK believe the government is handling it well. In a liberal society the government needs the support of the nation.