Pretty simple actually, if you are treating someone for severe symptoms you would have to get around to diagnosing a cause.
The UK has two separate distinctions for classifying covid deaths. "due to covid" which is where the virus was the underlying cause of symptoms and death, and "involving covid" where the patient was covid "positive", but the underlying cause of death was determined to be of other cause. As stated before, you could be determined covid positive. Which might mean you are just carrying some dead covid cells, ok I get that. But to be classified as having died due to covid it has to be relevant to symptoms and virus patterns, and determined by a medical professional.
Now that being said it would answer why the death rate has appeared to drop. If the threshold for testing positive was too low, you would get skewed data due to being positive and dieing from covid are measured in different ways.
To put it in simple terms, the CFR % is the deaths divided by cases. If the cases were over stated, then the CFR would indicate lower than actual. ie 1000 test positive vs 100 dead, 10% CFR. If only 500 of those actually carried enough virus to be deemed "infected" the real CFR is closer to 20%. Don't also confuse asymptomatic with non infected. Asymptomatic just means you are not displaying symptoms, but your body could be still fighting the infection within. Where as non infected would mean you are killing all virus cells that enter before they can replicate at any significant rate, both you could detect virus cells within the body.
BTW, to avoid any suggestion of conspiracy here; If a doctor was to deceivingly diagnose you with covid, you were treated for that, and later it comes out you died from flu, well, there would be a lot of law suits happening. I can't see doctors en-masse agreeing to waste their medical credentials and livelihood on pushing some weird government agender.