salaam,

Yaqub wrote:

Is it haram to wear a wig over the hijab?

Cos there used to be a Muslim women barrister in my old workplace, but I didn't think it was polite to ask if she put the white wig on top of her hijab.

Wigs and Hairpieces
In the category of female adornments, the addition of any other hair, real or artificial, to one's own hair—that is, the wearing of wigs and hairpieces—is also prohibited.
It is reported by al-Bukhari on the authority of 'Aisha, her sister Asma, Ibn Mas'ood, Ibn 'Umar, and Abu Hurairah that "The Messenger of Allah (peace be on him) cursed al-wasilah and al-mustawsilah," al-mustawsilah," wasilah denoting a woman whose profession is making wigs and hairpieces' and mustawsilah a woman who uses them.
Men are prohibited such things to an even greater degree, whether they are a wasil (coiffeur or hairdresser) or a mustawsil, like today's effeminate, long-haired young men of the "hippie" mould.
The Prophet (peace be on him) was very strict in combating such deceptions, so much so that if a woman lost her hair due to some illness, he did not permit her to add other hair to that on her head, even if she were soon to be married. Al-Bukhari reports 'Aisha's narrative concerning a girl of the Ansar who was married and subsequently fell ill, losing her hair. Some people wanted to add other hair to her own, but when they asked the Prophet (peace be on him) about this he replied, Allah has cursed the wasilah and the mustawsilah (Reported by al-Bukhari, in his book Clothing, in the chapter entitled "Adding to the Hair")
Al-Bukhari also reports Asma's narrative concerning a woman who said to the Prophet (peace be on him), "O Messenger of Allah, since my daughter has had measles, her hair has fallen out, and I am about to give her in marriage. Shall I add some strands of hair to her hair?" and the Prophet (peace be on him) replied, "Allah has cursed the wasilah and the mustawsilah. (Reported by al-Bukhari.)"
Sa'id ibn al-Musayab narrated that Mu'awiyah delivered a public address during his last visit to Madinah. In the course of it he took out a strand of hair, saying, "I have not seen anyone using this besides the Jews. Indeed, the Prophet (peace be on him), referring to the adding of hair to one's own hair, called it forgery." According to another report, he said to the people of Madinah, "Where are your scholars? I heard the Prophet (peace be on him) prohibiting the use of this and saying, 'The Children of Israel were destroyed when their women started using this.' "
The Prophet's terming the use of false hair "a forgery" indicates the reason for its prohibition. It is, in fact, fraud, falsification, and deception, and Islam condemns deception and dissociates itself from those who practice it either by material or psychological means, for "The one who deceives us is not of us." (Reported by a number of sahabah (Companions of the Prophet).)
Khattabi said, Harsh punishments are promised (in the Hereafter for such practices because they involve deception and fraud. If any of these is allowed, the door will be open for other types of forgeries. Moreover, this involves the alteration of God-given features, as mentioned in the hadith of Ibn Mas'ood concerning 'The alterers of Allah's creation. (Fath al-Bari, in the chapter entitled "Adding to the Hair.")
What is prohibited in these ahadith is the addition of other hair whether natural or artificial, to one's own, as this is a form of deceit and fraud. What is not included in this prohibition is the use of material other than hair, such as thread or cloth, which can be interwover with natural hair. On the authority of Sa'id ibn Jubair, we have the saying of the Prophet (peace be on him): There is nothing wrong with tawamil, (Mentioned in Fath al-Bari on the authority of Abu Daoud.) meaning the use of wool or silk to make braids. Imam Ahmad bin Hanbal haalso commented on its permissibility. (Fath al-Bari.)

Now if we apply the barrister wig situation to what this scholars says then no it would not be haraam. The reason being that she is not wearing the wig to deceive anyone nor is it for beautification purposes. The wearing of that ugly costly (i think its like £100 quid!) white wig is part of her profession.

w/salaam