The Shulchan Aruch (Yoreh Dei'a 97:1; listen to audio for precise citation) writes, based on the Gemara in Masechet Pesachim (36), that one may not knead dough with milk, as somebody might unwittingly eat the bread with meat, in violation of the prohibition against eating meat with milk. If bread was prepared with milk, it is forbidden for consumption, even by itself, without meat.
The Shulchan Aruch does, however, mention two exceptions to this rule, two situations in which it would be permitted to eat dairy bread. First, if the bread prepared with milk is small enough that it can be eaten in a single sitting, it is permissible for consumption. In such a case, there is no concern that one may eat the leftovers with milk, and hence one may partake of this bread. Secondly, one may eat dairy bread that has an unusual shape or form, that will serve as an obvious indication that it differs from normal bread. The Talmud gives the example of bread shaped long and narrow, like the eye of an ox. In such a case, the bread is permissible because there is a clear indication of its dairy status.
Would it be permissible to bake and eat dairy bread during the nine days (from Rosh Chodesh Av through Tisha B'Av), when eating meat is forbidden? One might argue that during this period we need not be concerned of somebody mistakenly eating the bread with meat, and this bread should therefore be permissible.
Nevertheless, the Badei Ha'shulchan (contemporary work of Halacha by Rabbi Feivel Cohen) brings that one may not bake or eat dairy bread even during the nine days. Since eating meat is allowed during this period under certain circumstances, such as on Shabbat and at a Se'udat Mitzva (a meal that involves a Mitzva), there is, indeed, the concern that one may partake of this bread with meat.
In light of this Halacha, there is room to question the status of Thomas' English Muffins, which is baked with milk. Although the package does, indeed, contain a symbol of Kashrut certification, one might question whether they are permissible for consumption. Perhaps one could argue that the unique form of the muffins the "nooks and crannies" suffice as a deviation from the standard appearance of bread to render them permissible, though this is questionable, since it cannot necessarily be verified that other kinds of bread do not share these external properties.
In general, one must ensure when purchasing bread from a gentile baker that the bread is Parve and was not baked with any milk.
Summary: One may not prepare or eat dairy bread, even during the Nine Days, when the consumption of meat is forbidden.
