You have no realistic chance of success with this.
If your speedo was broken and you knew it you should, by law, have stopped driving and had the vehicle recovered. No, I know few people would do so, but that that is what you would be told if you tried to use your broken speedo as a defence against a speeding allegation.
For the same reason it would be unwise to use the defective instrument as mitigation. If it is taken into account by the court it will, if anything, aggravate the offence. Imagine your cross examination in court:
Prosecutor: “So, Elijay, you knew your speedometer was broken”
Elijay: “Yes”
Prosecutor: “So you knew you had no means of accurately measuring your vehicle’s speed?”
Elijay: “Yes”
Prosecutor: “And despite this, you continued to drive?”
Elijay: “Yes”
Prosecutor: “And despite all this you expect the court to find you not guilty of speeding?”
Elijay “Err...Err...Err...”
If you opted for a court appearance and pleaded not guilty you would almost certainly be convicted. You would face a fine of about half a week’s net income, plus costs of about £350 (high because the matter was prepared for trial) plus a Victim Surcharge of £15 and three points.
Pay the £60 and either do the course or take the points, whichever you consider to be least inconvenient.