The responses so far cover most of the elements of what was required when my wife and I travelled to England in January:
a. we required a negative PCR test to fly, and a further negative PCR test to leave isolation when we arrived in the UK. We tested at Heathrow on arrival and were allowed to travel to our accommodation to isolate. We could have travelled from Heathrow to our accommodation first, and tested there. Either way, we had to have a test booked to complete the UK Passenger Locator Form which has to be completed before travel. The PCR test results took about 36 hours both times we tested (on arrival and before departure). On arrival, during this time you are not allowed to leave your accommodation. We were fortunate to be staying near our son and daughter-in-law, who arranged for a food parcel to be ready for us when we arrived. Getting meals delivered would also have been an option.
b. The rules for travel from the UK to Australia changed while we were in England. We knew this might happen, and had been holding out from booking the tests for our return travel, but as soon as we had booked the slightly more expensive PCR tests, the Australian Government changed the rules to allow rapid antigen (aka lateral flow) tests. There was a price difference of about 15% between the two type of tests at the lab we used.
c. Tests need to be done by a recognised lab, and self-administered tests will not be accepted. When checking in, we saw passengers ahead of us sent of to see if they could get a rapid test at the airport when they attempted to use self-administered test results. I didn't see them again, so I can only hope that they got their results back in time to be allowed to board.
d. On arrival in Australia, we were required to isolate until we had a negative test, which could have been either PCR or RAT. We use RATs we had obtained in the UK while we were there, so we could do this as soon as we had arrived in Sydney at the end of our international flight legs. As a result, we were not required to isolate any longer once we arrived home.
For the OP, you might find that a large part of your 'couple (of) days' in London is taken up in isolation if the isolation rules don't change and you still need to do a PCR test. There may be services that can provide results sooner than we experienced, but expect to pay more for that.
I wholeheartedly agree with the advice that things can and will change. Having a general idea of what might be required is fine, but detailed arrangements shouldn't be contemplated until much closer to one's travel dates.