Actually, in the interests of transparency, they don't legally have to refer to someone else immediately.
The GMC "Personal Beleifs and Medical Practice" guidance states:
" 21. Patients may ask you to perform, advise on, or refer them for a treatment or procedure which is not prohibited by law or statutory code of practice in the country where you work, but to which you have a conscientious objection7. In such cases you must tell patients of their right to see another doctor with whom they can discuss their situation and ensure that they have sufficient information8 to exercise that right. In deciding whether the patient has sufficient information, you must explore with the patient what information they might already have, or need.
22. In the circumstances described in paragraph 21, if the patient cannot readily make their own arrangements to see another doctor you must ensure that arrangements are made, without delay, for another doctor to take over their care. You must not obstruct patients from accessing services or leave them with nowhere to turn. Whatever your personal beliefs may be about the procedure in question, you must be respectful of the patient?s dignity and views.
23. You must be open with patients - both in person and in printed materials such as practice leaflets - about any treatments or procedures which you choose not to provide or arrange because of a conscientious objection, but which are not otherwise prohibited. " <a class="break-all" href="http://www.gmc-uk.org/guidance/ethical_guidance/personal_beliefs.asp" rel="nofollow" target="_blank">www.gmc-uk.org/guidance/ethical_guidance/personal_beliefs.asp</a>
So, if a Doctor believes that a patient is able to sort out an alternative appointment, they can just direct them to do so. If they feel that they are unable to do that themselves, then they must ask another doctor to see the patient immediately.