If I land in London the night of September 9th, will I be required to self isolate until September 22nd or September 23rd?

The top answer so far quotes the guidance and not the law.

The law is The Health Protection (Coronavirus, International Travel) (England) Regulations 2020, and specifically Regulation 4(7)(a)

(7) P must, on their arrival in England, travel directly to the place at which they are to self-isolate, and must then self-isolate until whichever is the earlier of—

(a) the end of the 14th day after the day on which they arrive in the common travel area, or
(b) their departure from England.

The fourteenth day after your arrival is 23 September, and the Regulation means that the quarantine period is 14 full days which start when you arrive, but are counted from the midnight after you arrive. If you arrive on 9 September, the remainder of that day and the period 10–23 September is your quarantine period and it ends at 2359 on 23 September.

How you choose to act in the last hours of your quarantine (which will be out of normal working hours) is of course entirely up to you.

A strict reading of the rules simply says 14 days, and as such the sensible thing to do would be to consider that 14 full 24 hour periods, so if you entered the country at 8pm (for example) on the 9th of September, then your isolation period would end at 8pm on the 23rd.

This isn't the sort if thing to skimp on, keep yourself and others safe.

From a legal perspective, the fourteen days start on the day after your arrival (the legal text is here, see 4.(7)(a)), so legally you are required to self isolate until the end of day on September 23rd. That is, strictly speaking (from a legal perspective) you should not attend the event if you arrive on September 9th.

The remainder of this answer discusses where the 14 days comes from.

From a disease transmission perspective, there is no magic event after an exact 14 days. The 14 days is an estimate of when about 99% of people will have shown symptoms assuming they were infected on Day 1.

There are estimates of the distribution of incubation periods, for example look at the figure in this paper.

Another study (here, not peer reviewed) suggests that 'about 10% of patients with COVID-19 would not develop symptoms until 14 days after infection'.

Yet another study (here) suggests that the incubation period depends on age (see Figure 1 in said article).

Self isolation is just one aspect of prudent Covid behaviour. If you attend your event wear a mask and maintain distance if for no reason other than the precautionary principle.