As a Zimbabwean citizen, you should apply for an Emergency Passport that allows for a one time trip back to your home country. Note that sometimes an exit visa may be needed by the host country (South Africa) or by any third country you may be travelling through.
Should this not be possible: the reason why the passport cannot be issued, in writing, should ...
If you want a passport from another country, that usually means becoming a citizen of that country. This is usually rather difficult, and in most cases getting a new passport from your old country will be much easier than getting a new citizenship.
You should submit your application, with as many details of the denial as you remember.
You are not the first person who has mislaid, never got or plainly thrown away the denial letter. It is quite a normal thing even.
As long as you are open about the fact you got a denial, and tell when (as good as you can) so they can check back if they feel the need.
Assuming you hold a Travel Document Under the Convention of 1951, inputting your data into Timatic, the database used by airlines yields the following results:
United Kingdom - Destination Visa
You will need to apply for a Standard Visitor Visa.
Instead of sending the visa refusal with your application, write a note saying:
you're perfectly aware it should've been included
you don't have it
you asked for a copy
they claim not to have it either
They won't expect you to work miracles, they expect you to be honest. So be honest. Provide them with the details you have (like you have posted ...