The Contempt of Court Act 1981 is used to protect the integrity of the court and is used to prevent unruly behaviour “in the face of the court” (e.g. interrupting proceedings) or to prevent publication of inappropriate reports on proceedings. Strictly speaking it could be argued that deliberately refusing to answer bail is “Contempt of Court”. However, that would probably involve interpreting the 1981 law more widely than is usual, Also, a perfectly acceptable alternative exists in the Bail Act and your friend would almost certainly have a charge under that act levelled against him when he surrenders.
If, as is likely, a warrant “without bail” is issued by the judge your friend will be taken into custody when he surrenders himself (if he is not arrested beforehand) and held until he is produced before the court. In sentencing for the Bail Act offence the judge will consider the reason for non-attendance and the consequences. From sentencing guidelines “Deliberate failure to attend causing delay and/or interference with the administration of justice” a “starting point of 14 days custody is suggested. There is no doubt that his absence will be seen as deliberate. What effect it has on the administration of justice (bearing in mind that the hearing is pre-trial) is for the judge to decide.
In addition, as has been suggested, your friend’s bail could be withdrawn, leaving him in custody until the trial date. However, this should have little or no influence on the sentence for the substantive offence (assuming he is convicted).
Your friend should think long and hard about his proposal to absent himself. He has asked for a change of date and has been refused, and this will not sit too well with the judge. He may find himself spending some time in custody.