If it's not possible to obtain the consent of everyone who has Parental Responsibility for your child, then it is advisable to seek the services of a professional mediator (a form of Alternative Dispute Resolution). If this isn't practical, or mediation fails to reach a satisfactory resolve, then the next step is to seek a court order.
If granted, a court order allows the name of a child to be changed without the consent of the other party. The type of order that would need to be applied for is called a 'Specific Issue Order'. This type of order gives direction on a specific point relating to your child's life, in this case, their name.
To apply for a Specific Issue order you would need to complete form C100 and submit it to a local court that deals with family matters. At the time of writing the applicable court fee is £210, although it's possible to claim a fee reduction, depending on your individual circumstances.
You can find a court in your area using the court finder website: http://hmctscourtfinder.direct.gov.uk/HMCTS/
It should be noted that a court order will only be granted whereby the name change is considered to be in the 'best interest of the child'. Infact, there is an implicit bias on the side of the courts not intervening because section 1(5) of the Children Act 1989 reads:
"where a court is considering whether or not to make one or more orders under this Act with respect to a child, it shall not make the order or any of the orders unless it considers that doing so would be better for the child than making no order at all."