The numbers I ran for the UK put it at 12 years:

No. People in UK: ~66,000,000

Est. proportion of people who will get sick: 80%

Est. proportion of sick people who require intensive care: 5% (in Italy it's 10%)

So that's 60,000,0000.80.05 = 2,640,000

Number of ICU beds in the UK: ~4100 (90% occupied, but let's ignore that for now)

Length of time ICU required: at least 1 week (probably longer, but let's ignore that too)

So that's 2,640,000 / 4100 = 644 weeks or 12 years that we would need to spread the cases over in order to have enough capacity.