From the CPS website:
"Grievous bodily harm means really serious bodily harm. It is for the jury to decide whether the harm is really serious. However, examples of what would usually amount to really serious harm include:
injury resulting in permanent disability, loss of sensory function or visible disfigurement;
broken or displaced limbs or bones, including fractured skull, compound fractures, broken cheek bone, jaw, ribs, etc;
injuries which cause substantial loss of blood, usually necessitating a transfusion or result in lengthy treatment or incapacity;
serious psychiatric injury. As with assault occasioning actual bodily harm, appropriate expert evidence is essential to prove the injury"
A single broken finger (with a clean break, rather than a compound fracture) would almost certainly fall under 'ABH', rather than 'GBH'. It would up to the CPS (initially, and then a court eventually) to decide whether 'GBH' would be relevant where several fingers were involved. From cases I've seen reported in the press though, I'd still think that 'ABH' would be the most likely charge.