Point 1:
You can't change your son's birth certificate. (Some amendments to birth certificates are, under certain circumstances, possible but the change you suggest isn't one of them).
Point 2:
As you already seem to have discovered, anyone with parental responsibility must give their permission before a child's 'official' name can be altered:
http://www.direct.gov.uk/en/Parents/ParentsRig hts/DG_4002954
Point 3:
While your son must (unless his father agrees otherwise) retain his current name for 'official' purposes (e.g. when you apply for a passport for him), you can call him any name you choose. When I was teaching we had dozens of pupils who might, for example, have been 'officially' named as Mark Smith but who was always known (to staff and pupils alike) as Mark Robinson. The only time that can be a problem is when a secondary school enters pupils for public examinations (e.g. GCSEs). It's then a requirement that the young person's 'official' name is used (and that name will appear on the resulting exam certificates).
So your best option (unless you can get the father to agree to a change) is probably to retain your son's official name but to simply call him by the name of your choice. Just make sure that his future schools are aware of the situation. (As I've suggested, most schools will have several pupils in every year group with both 'official' and 'unofficial' names). If your son so chooses he can always make the 'official' change (by deed poll) when he becomes an adult.
Chris