Just reading a bit more about when beauticians can refuse to serve someone of the opposite sex.
www.whatdotheyknow.com/request/525230/response/1298678/attach/html/10/WhatEqualityMeansForYourBusiness%20CombinedDocs%20Redacted.pdf.html
This says:
You are allowed to provide separate services for men and women where providing a joint service (ie one where men and women are provided with exactly the same service) would not be as effective. You are also allowed to provide separate services for men and women in different ways or to a different level where:
• providing a joint service would not be as effective, and
• the extent to which the service is required by one sex makes it not reasonably practicable to provide the service except in the different ways or to the different level.
In each case, you need to be able to objectively justify what you are doing.
You are allowed to provide single-sex services (services just for men or just for women)
where this is objectively justified and:
• only men or only women require the service, or
• there is joint provision for both sexes but that is not enough on its own, or
• if the service were provided for men and women jointly, it would not be as effective
and the extent to which each sex requires the service makes it not reasonably practicable to provide separate services for each sex because of the extent to which the service is required by persons of each sex, or
• the services are provided in a hospital or other place where users need special care,
supervision or attention (or in parts of such an establishment), or
• the services may be used by more than one person at the same time and a woman
might reasonably object to the presence of a man (or vice versa), or
• the services may involve physical contact between a user and someone else and that other person may reasonably object if the user is of the opposite sex.
So this case would surely be covered by the physical contact element, though most people if not religious would probably be OK with touching the hands of someone of the opposite sex.