Sure it did.
Let's assume the infected population grows as s(x)=1/(1+e^-x). About 99% of the curve lies from -5 to 5, so let's ignore the rest to simplify the math. Let's then assume that 99% of the people are infected over the course of 180 days, so 1 day is h=10/180=0.055 on s(x). That's a decent attempt at "flattening the curve".
The curve goes from 0 to 1, so if for example s(h/2)-s(-h/2)=0.014, this tells you that around the peak of the infection, 1.4% of the infected population will get the disease in a single day. With 70% of the population getting infected, that's a lot of people (about a million in a single day).
Let's be super optimistic and say that 70% of people getting it means 7% having symptoms and 0.7% needing an ICU bed (younger people also get bad cases, even though the median age of death is high; they just survive thanks to the treatment). Problem is they will need it for 3 weeks (~20 days) so you need a lot of beds.
Specifically s(10h)-s(-10h) = 0.27, that is, 27% of the infected population will get the disease in the 3 weeks around the peak. At this point 27% * 70% * 0.7% of the UK population needs ICU beds at the same time.
That's 80000 people, but the country has just 4000 ICU beds. Those that couldn't be treated would die, and that's just in the 3 weeks around the peak.
It's safe to say that for most of those 6 months the NHS would be so overwhelmed that close to 0.7% * 70% of the UK population would die. It's a back of the envelope calculation, only the order of magnitude makes sense. But still, it's in the hundreds of thousands.
So yes, unless Johnson could find tens of thousands of ICU beds in the next few weeks (because the numbers would reach 10000 or so long before that peak point) those many people would die from lack of treatment. And the NHS would be completely clogged, so more people would die preventable deaths due to lack of room for treating non-COVID-related patients.