.. when asking why we're not seeing more cases or deaths.
It won't be a 'second spike' - the 'spike' was the BIG thing back on 8th April. The plan is avoid that completely. We might see an increase in cases (and ultimately in deaths), but that's not going to happen while we are all still quite far apart.
Majority of the country is still far apart. Even though stuff is opening, it's nowhere near 'normal'. People aren't rammed together in pubs, clubs, schools, lecture halls, trains, buses, concerts etc, and we're not having the same number of flights arriving by any stretch of the imagination, let alone from places that have lots of infected people, so it's not going to be being caught nearly so much.
If a rise in cases is going to happen, it'll be when we all relax more, when there are no rules around what can be open and so on, and probably when the weather is more conducive to life being indoors. Not just because someone sat outside their house on VE day.
I'd say that the death figures not dropping for ages is probably more about those sorts of things happened - kept it bumbling along for longer than it might have done, when unlucky people caught it around the beginning of May.