The key issue with any measures to relax the lockdown is how much they affect the R0 virus transmission value. Without any social distancing measures, R0 was about 2.5 (each infected person gives it to 2.5 others on average), resulting in exponential growth in infections. I believe that the current UK lockdown has been estimated to have reduced R0 to about 0.65.
If the full lockdown is maintained long enough, this will lead to a steady decline in cases and death rates. But any relaxation will increase R0 again, slowing or reversing the decline.
The highest tolerable R0 would be 1 - above this cases will accelerate again until critical care capacity is overwhelmed or a lockdown reimposed. But R0=1 will maintain cases at a constant level indefinitely - or at least until a vaccine is available or herd immunity develops, likely more than a year best case.
The big dilemma is that the earlier the lockdown is eased, the higher the ongoing death rate will be. If we ease off as much as possible at the peak, allowing R0 to increase to 1, the death rate will likely remain above 1000/day for months. Within the NHS capacity, but are we willing to tolerate that? At the other extreme, if the full lockdown is maintained for several weeks longer, it might be possible to get the death rate down to 100/day or less and then keep it there, with the same R0=1 easing measures. But are we willing to tolerate the additional damage to the economy and (other aspects of) public health from such a long lockdown?
An intermediate level of easing at the peak might give a R0 of, say, 0.9. Then there would be a slow decline in death rate, but many more deaths in total than from a prolonged lockdown.
An unenviable choice for policymakers, with the interests of different sections of the population in conflict (e.g. affluent pensioners, at risk from the virus, versus young families, at risk from the economy).
It appears that the government is considering mass testing plus contact tracing and quarantining, as in China and S Korea, as part of the exit strategy. This can potentially reduce R0 much more than social distancing measures alone, and so enable more easing. The catch is that contact tracing in the UK would only become feasible if we first drove infections down to a very low level through a prolonged lockdown, as the Chinese have done in Wuhan. No gain without pain!