The law requires the information to be provided within 28 days beginning with the date of service (unless it was not reasonably practicable to do so).
Service is when the notice is delivered to the addressee's last known address. It is deemed to have been effected 2 working days after posting unless the contrary is proven.
If you plead guilty but mention in mitigation that the notice was delivered late and that you responded as soon as possible afterwards, the court ought to reject your plea and enter a plea of not guilty on your behalf.
To defend this, you would have to persuade the court, on the balance of probabilities (more likely than not), that the notice was delivered late/misdelivered.
If you plead guilty to lessen the punishment (other than the question of whether that would constitute perverting the course of justice), you would receive a 1/3 discount off the fine - so would face 6 points (MS90 endorsement code - which is likely to see insurance go up), a fine of 1 week's relevant weekly income (after tax and NI), 40% surcharge and ~£90 prosecution costs.
If you defend and win, no fine, no points, no costs.
If you defend and lose, would lose discount on fine (and surcharge on fine), so 1.5 x RWI and 40% of that, and prosecution costs would be ~£620.
As regards defending, independent/official documentary evidence of ongoing postal issues is worth its weight in gold - although the primary evidence would be your testimony.
