The Geezer is right in that these prosecutions are becoming more common.
However, if it is prosecuted, your chances of acquital are slim. The wording of the Act says that careless driving is that "which falls below that expected of a careful and competent driver".
Simply, careful and competent drivers do not pull out from a side road into the path of a vehicle travelling on the main road. Similarly they do not collide with the rear of the vehicle in front (and these "accidents" are also seeing an increasing number of prosecutions).
The decision by the CPS whether or not to prosecute will be taken before you enter your plea, so the "inconvenience" you may cause by maintaining your innocence will not influence that decision.
If you are taken to court and maintain a not guilty plea, your sentence if convicted will be higher and you will be liable for prosecution costs of about �250 (instead of about �45 for a guilty plea).