lcg is not correct.
You can submit to the Magistrates a plea that there are “Special Reasons” why you should not have points imposed on your licence. You are, of course, guilty of speeding and you must enter a plea of guilty. But following that your mitigation can be put to the court for their consideration.
There are no hard and fast rules about what constitutes a successful Special Reasons argument. Every case is considered on its merits. The reasons put forward must be relevant to the offence itself rather than the effect the points would have on you, the offender. You should be prepared to explain to the court the precise details of why you found it necessary to exceed the speed limit and whether you had considered and dismissed any alternatives to your action (such as contacting somebody else to reach the location who may have been able to get there sooner than you). As Eddie suggests, to do this you should attend in person so that you can give the evidence on oath and be questioned about it.
As an aside, no judge will be involved in this decision unless the court is presided over by a District Judge (Magistrates’ Court). Outside London and a few other large cities District Judges are to be found exceptionally and the matter will almost certainly be decided by a bench of three lay magistrates.