Rab Hid"a, 'a"h, writes in Mahziq Berakha that even though the Taqanah (edict) of Ezra HaSopher, 'a"h, was that we must wash clothes for Shabbath on Thursday, it doesn't mean Thursday alone. The reason he mentioned Thursday is to exclude Friday. However, if someone wished to do the laundry for Shabbath on Wednesday, that would be permitted.
It says in Meqabsiel that, nevertheless, washing clothes on Thursday is the most appropriate, because it is more obvious that it is being done in honor of Shabbath. If one washes on Wednesday it is less obvious, but there is no need to protest if someone does their wash on Wednesday. According to the Qabbalistic understanding, as explained by Rabbenu the Ari, z"l, preparation for Shabbath begins on Wednesday.
In view of this, there is no problem if one wishes to wash on Wednesday. However, since Tuesday is considered as belonging to the previous Shabbath, it is not appropriate to wash on Tuesday for Shabbath, Additionally, it is so far away from Shabbath that it will not be apparent that the wash was being made in honor of Shabbath. In view of this, one who is accustomed to doing a wash on Tuesday for Shabbath, should do it instead on Wednesday or, ideally, Thursday.
(See Meqabsiel, 2nd year, Lekh Lekha, Oth 15)
Mekavtziel, Meqabsiel, shabbath, laundry for shabbat, shabbos, Laws of Shabbat