I'm probably missing something here but given that most if not all the possible contributing factors postulated by many on the thread - poor / over crowded housing; cultural differences - existed way before C19 arrived what delayed the huge surge in cases in Leicester until quite recently, or rather did something else alongside existing factors light the touch paper.
The peak of case numbers - as published at least - in England was pretty much first two weeks in April. From the published PHE case figures - vast majority pillar 1 at that time - based on specimen date there were around 45 cases per 100,000 both week ending 5th and 12th April, declining a bit to just under 40 w/e 19th ; and around the 30 mark by w/e 26th April, and down to low 20s for w/e 3rd May
Leicester had a cases per 100,000 rate of: 42, 45, 27, 31 and 23
Leicester was therefore spectacularly average.
I know some will argue that Covid-19 had not made it out of London yet; stuck in traffic on the M1 somewhere near Milton Keynes or held up by signalling work on the railway outside Wellingborough.
I would counter by suggesting look at:
Cumbria - 84 cases per 100,000 in both w/e 5th and 12th April; and still over 50 w/e 19th.
Sunderland - 100, 115, 86 cases per 100,000 in those three weeks.
Knowsley 85, 88 and 72 cases per 100,000 in those three weeks
If there was a genuine "lockdown guidance does not apply to us" mentality would this have not been prevalent from the outset?
So why the delay in Leicester, and the delayed surge? Was there actually a quite good compliance with lockdown for the best part of two months and then suddenly a widespread "sod it" ? Or did the initial relaxations, due to some of those specific local conditions, perhaps make a surge inevitable?
If it is still there the Leicester Mercury had a great graph of cases over time.
As others have rightly said the data , as far as possible, needs to be made public so what happened and why can really be understood - and avoided for the future.