With the poor to inaccurate death toll figures and the lack of testing ability do the daily figures seem likely to be worth reading as "over the initial peak"? It strikes me as a hopeful or even misleading situation.
If you dont trust the death figures for that then use the hospitalisation and intensive care number (or number of ambulance call outs in Scotland) as additional evidence. The all point in the same direction, absolute peak in deaths was weeks ago (around April 8th) but the decline since then is somewhat slow and modest, which sadly was expected.
In terms of judging actual number of deaths and exact timing, I will wait for data that takes longer to accumulate, such as ONS data (and equivalents for Scotland and Northern Ireland). Final numbers with which I could judge entire excess deaths over the period, thus not missing any deaths that havent been listed as Covid-19 related, take a long time. But provisional ones come out every week, and so there are already some signs of scale of other deaths. I'll know quite a bit more about Aprils peak of deaths when the provisional monthly report for April comes out from ONS on May 28th, because if the format is the same as their March report, it will have some numbers I can use to ascertain daily figures from (for all deaths, not just ones actively labelled as Covid-19 on death certificates, which will still be an undercount).
With data thats available now, peak number of deaths from NHS England & Wales hospital figures is 831 on 8th April, though this number is still being adjusted every day (it was still below 800 last time I mentioned it). If I use provisional ONS data instead, I inevitably get a higher number for that date because ONS figures arent just hospital deaths, a figure of 1,021 as of last Tuesdays published ONS data. If I add in Scotlands data from National Records of Scotland then I get a figure of 1111 deaths for that day. The five days before that date will also end up being over 1000 (a few are currently just 2 or 5 below 1000), but these numbers will all evolve further in future and I can say less about days after 8th April since such dates have even more data yet to come in for them.
Anyway I dont like assumptions so it is always possible the absolute peak day of deaths may change a bit in future, but I would be a bit surprised if it turns out not to have been very close to the date indicated by the current data.