"I don't understand where this idea is that the peak will be different in different places, as though it is some wave that moves from place to place."
Different areas of the country can have different start dates, curve forms, daily death peaks etc because the country does not behave homogeneously
This is far more obvious in the USA, with the diferent states and measures, but also applies within the UK to a lesser extent
e.g. some areas will have had mass public events at certain dates, e.g. Crufts, Cheltenham
some will be more rural, where infection spread is lower and slower
some will have rapid spread due to international links - airpots, ports
different age demographics between e.g. Cornwall and London
The "national trend" is a summation of all the local trends in Uk cities and town and rural areas