The police will not be interested in “delivering justice to the actual criminal” for the simple reason that they don’t know who it is. It was your duty to tell them.
“… but trying to criminalise me for his crime and because I never replied to a letter.
They are not criminalising you for his crime. They are charging you with the one you committed - specifically “failing to provide driver’s details.” This is an offence under Section 172 of the Road Traffic Act. On conviction, it carries a hefty fine, six points and an insurance-crippling endorsement code which will see your premiums increased considerably for up to five years.
Unfortunately your only option, apart from pleading guilty, is to defend the charge on the basis that it was not reasonably possible for you to reply because you did not receive the request.
Your explanation for that does not sound too convincing. You may not have seen the request, but it was deemed “served” on you two days after posting. The police will undoubtedly be able to prove when they posted it, leaving you to prove to the court’s satisfaction that it did not arrive.
From the brief explanation you have given here, I don't rate your chances of success too highly. Do you have any evidence of a general problem with the post at your home address which might support your claim that the request was not received?