These things are very difficult to predict. On the present trajectory, I shouldn't be too surprised if the Government's hand were forced in around late August/September, but we'll have to see.
If there is a clear case for another lockdown, then it feels difficult to see how any decision the Government makes could make it look good. Either having one when we were promised an effective end to this cycle, or not having one when it's clearly necessary to prevent thousands of excess deaths, would be likely politically disastrous.