Technically, you received an SJPN for the speeding offence. You were offered an alternative disposal (the COFP), but [on the face of it at least] failed to comply with the requirements to accept it. We see this a lot.
Personally, I am not entirely convinced that paying online does not satisfy the statutory identification requirements, which would render subsequent prosecution unlawful, but the courts have historically been slow to find that the police have made such widespread fatal errors (floodgates), and anyone who failed to read the notice properly, and therefore found themselves in this position, is probably not the best person to run such an argument.
For the sake of completeness, if the statutory requirements to accept the COFP are complied with, the driver cannot lawfully be prosecuted. They are set out in section 75 of the Road Traffic Offenders Act 1988. Basically, other than not being liable to tot up, payment has to be made to the appropriate person within the suspended enforcement period (28 days from date of issue), and the identification details have to be provided to the appropriate person within the same period. For the purposes of payment, the appropriate person is the fixed penalty clerk. For the purposes of the identification information, the appropriate person is the fixed penalty clerk. The requirement for identification information is satisfied if either the appropriate person is satisfied as to your identity, or you provide the appropriate person with your name, licence number and date of birth. A UK licence number incorporates the holder's date of birth (albeit only 2 digits for the year - unless this has changed for those born 2000 onwards).