The situation you described is EXPLICITLY addressed in Paragraph 12 of the Immigration Rules, which says...
12.A person claiming to be a British citizen must prove that he has the right of abode in the United Kingdom by producing either: (i) a
United Kingdom passport describing him as a British citizen or as a
citizen of the United Kingdom and Colonies having the right of abode
in the United Kingdom; or (ii) a certificate of entitlement duly
issued by or on behalf of the Government of the United Kingdom
certifying that he has the right of abode.
Which means that they expect to see a British passport. The other proof that someone can use is a 'certificate of entitlement', which is a stamp that goes in your foreign passport. These are fairly rare, and you must apply for a certificate well in advance anyway. A naturalisation certificate is not going to be that helpful because it is not listed in Paragraph 12, and naturalisation certificates require an examiner to adjudicate their authenticity.
Note also the precise wording of the rule which does not stipulate that the passport be current.
South Africans need a UK Entry Clearance prior to arrival, and if you do not have an Entry Clearance and your only travel document indicates that you need one, you would expect to get bounced (unless you are a silver-tongued genius). But the problems would most likely not come from a British Immigration Officer, but rather your carrier, who can refuse to board you. The carrier faces a fine and embarrassment for bringing in an insufficiently documented migrant.
To be clear, Brits lose their passports all the time for all manner of reasons. Having a lost passport kicks off a procedure that is fairly mechanical. It's different than having no passport.
On the bright side, if you are resident in the US, then you can use the British Consulate General in New York to apply for Entry Clearance. Once you have permission to enter the UK, you enter and then take advantage of Paragraph 14 of the Immigration Rules (for which your nationalisation certificate will be helpful).