Some back-of-a-fag-packet maths:
The UK started lockdown on Tuesday 24 March.
If you assume that there's a 14 day lag for new measures to be reflected in reality and that the number of cases will keep rising by about 30% per day, the peak for positive test results would be on 11 April.
Since the incubation period is about 2 weeks, hospitals could then be under the most strain on around 25 April.
If the lockdown is successful and the cases rate increase then drops to 15% per day, it'll take till around 26 April to reach the numbers required for herd immunity (regardless of whether that's the aim or not, and assuming the real cases are 20 times as numerous as tested cases). Then another 2 weeks before those people can all leave self-isolation. So the UK could potentially begin to lift measures on 10 May.
If the country can somehow keep it together for 7 weeks, the nationwide crisis could be over as soon as then. Unfortunately, we'd be looking at over 1 million dead (assuming a 2% CFR, plus all those who can't get treated because of the NHS being over capacity). That's absolutely horrific, but I'm not sure if there's any way around it given what's happened up until now.