Unless a search is being carried out under the provisions of the Police and Criminal Evidence Act (and/or other relevant legislation) by a police officer (or by another 'official', such as as a customs officer), you always have the right to refuse to be searched. However, a private body, such as a nightclub, can make it a condition of entry that you agree to a search.
There's no specific legislation which prevents anyone conducting a search on a member of the opposite sex. (Remember that you must agree to the search anyway). However, professional codes of conduct will normally state that a search should only be carried out by someone who shares the gender of the person being searched.
If a search is carried out without the permission of the person being searched (other than by, say, a police or customs officer) the person conducting the search places themself at risk of being prosecuted for common assault. If the person conducting the search 'touches intimate areas of the body' he/she might also risk the possibility of charges of indecent assault. It's for that reason that the professional codes normally require that a man shouldn't search a woman (or vice versa). However there's no strict legal reason why someone shouldn't search a person of the opposite sex. (Equally, someone searching another person of the same gender isn't immune from a charge of indecent assault).
If a club's policy is simply that you agree to a search if you want to be admitted, it's perfectly reasonable for the club to add 'by a member of either sex' to its conditions, whether those conditions are explicitly stated or simply implicit because the only staff on the door are of the opposite sex to you.
Chris