You must all remember that the current measures aren't really in place to stop the infection spreading, but to slow it.
Therefore, this is a simple exercise in exponential growth leading to herd immunity.
Some figures.
Based on this article:
expert comments about herd immunity | Science Media Centre , the COVID virus requires 60% of the population to have the virus to provide herd immunity based on the virulence of the spread observed.
Therefore, to assure immunity of our assumed population of 70million, we need 42million people to get it and, not to be callous, either recover or die. Either is fine for our purposes here.
For exponential growth:
X(t) = X0 * b^t where xt is our end goal - 42mil cases, X0 is cases now, b is growth factor (new people infected by each current case)
For Covid-19, the groth factor can be extrapolated into the range of 1.1194 based on US data:
Modeling Exponential Growth
The UK has seem similar rates of spread, so all else being equal, this should be broadly equivalent.
Therefore, when will social distancing no longer be useful?
Solving for t in the equation above based on the current reported case load of 93,873 and that b value gives us a value of 54-55 days until herd immunity, assuming no tailing off of infection rate as we move towards this state. However, I'd argue that actual case load is a lot higher than reported, so we might be able to knock a day or two off this.
Based on this, and assuming we can't slow infection rates further through government intervention, social distancing will have little to no beneficial effect in lets say 65 days to allow for a tail on the b value later on in the growth phase. I make that 19/06/20. Let's assume a decent safety margin of 4 weeks for further tailing of the b value and government inertia in collating data and making a recommendation, then we should be out of lockdown by mid July.
Yes, it's possible that we can manage this longer and work towards a vaccine, but I can say with 99.9999% certainty that we will not have any meaningful medication within this few month time frame, so herd immunity is the inevitable end play.
Of course, the less fun part is that based on a 3% mortality rate (yes, the UK current reported rate is closer to 12%, but I believe that to be an error in reporting which means that the vast majority of cases, which are mild, are not diagnosed, leading to this inflated figure), we're looking at 1.26M deaths. Fun times.