The Shulhan Aruch (Orah Haim 179; listen to audio recording for precise citation) writes that once a person washed Mayim Aharonim, the washing before Birkat Ha’mazon, he may not eat or drink until after he recites Birkat Ha’mazon. The washing of Mayim Aharonim signifies the conclusion of the meal, and one must therefore immediately recite Birkat Ha’mazon. If he wants to drink another glass of water or take another bite of food, he must wait until after Birkat Ha’mazon.
The Shulhan Aruch then proceeds to address the case of a person who has not yet washed Mayim Aharonim, but already summoned the other people at the table to recite Birkat Ha’mazon. In such a case, according to the Shulhan Aruch, one may drink, since he has yet to wash Mayim Aharonim, but provided that he first recites a Beracha. Although he is not required to immediately recite Birkat Ha’mazon, his expressed decision to recite Birkat Ha’mazon at that point constitutes "Heseh Ha’da’at" – the diversion of his attention from the meal, and he must therefore recite a Beracha before drinking.
With regard to eating in such a case, the Shulhan Aruch cites a debate among the Rishonim (Medieval Halachic scholars). The Rosh (Rabbenu Asher Ben Yehiel, Germany-Spain, 1250-1327) equated eating with drinking in this regard, and thus required one to recite a Beracha if he wishes to continue eating after expressing his desire to recite Birkat Ha’mazon. Rabbenu Yona (Spain, 1210-1268), by contrast, held that expressing one’s desire to recite Birkat Ha’mazon does not signify his withdrawal from food, and therefore he may continue eating even without a Beracha. As opposed to drinking, which requires a new Beracha in a case where one had already expressed his decision to recite Birkat Ha’mazon, eating does not require a Beracha in such a case.
The Shulhan Aruch sides with the view of Rabbenu Yona, and therefore, strictly speaking, one may eat in this case without reciting a Beracha. However, given the difference of opinion in this regard, it is preferable for one to first recite Birkat Ha’mazon, so that he will be required to recite a new Beracha according to all opinions, thereby avoiding this controversy. Alternatively, if somebody else happens to be eating and must recite the Beracha in question, one may listen to his Beracha and have in mind to fulfill his obligation – according to the view that he is indeed obligated – through his fellow’s recitation. As mentioned, however, according to the strict Halacha one may continue eating without reciting a new Beracha in this case.
Summary: Once a person washes Mayim Aharonim at the end of a meal, he may not eat or drink anything until after he recites Birkat Ha’mazon. If he has yet to wash Mayim Aharonim, but verbally expressed his desire to recite Birkat Ha’mazon, then he may continue drinking, but he must first recite a Beracha. Ideally, he should not eat in this case until after Birkat Ha’mazon, but according to the strict Halacha he may eat, without a Beracha.
