I understand that lots of the herd die of whatever it is in the establishment of herd immunity.
That depends on the mortality rate of the disease. The mortality rate of COVID19 is said to be about 1% of those who catch it. The herd immunity level is supposed to be around 60% (compare measles, which is much more infectious at around 95%).
You can do the maths for the UK of approximately 68 million people.
To achieve herd immunity, you would need 68 million x 60% = 40 million (approx) to have had the disease. If 1% of them die, that's 400,000 deaths in the UK to achieve herd immunity. That's just the people who would have died of COVID19. There would be quite a lot of collateral damage including, for example, people who needed intensive care for other reasons but who couldn't get into hospital.
Then you have to consider what 400,000 extra deaths over a few months would look like. It would be the right time to buy shares in crematoria and cold storage facilities.
And the punch line is, of course, we don't know if herd immunity is even possible with this disease. There's no herd immunity for the common cold or influenza.