If a person is eating while walking in the street such as if one sucks on a candy, chews gum, or eats nuts as he walks it is clear that he does not have to recite a new Beracha every time he walks. Quite obviously, he has in mind at the time he recites the Beracha that he would change locations as he eats, and so he certainly does not need to recite a new Beracha as he walks.
This also applies to a person who begins eating or drinking at home but it is clear at the time he recited the Beracha that he plans to take the food or beverage with him. For example, if a person makes himself a cup of coffee as he is getting his coat and car keys, preparing to leave for work, and he recites the Beracha over the coffee at home before he leaves, he does not have to recite a new Beracha outside in the car. Since it is obvious that he plans on taking the coffee with him outside, he does not recite a new Beracha after he leaves.
If, however, a person eats at home, at the table, and then he suddenly realizes he needs to leave, so he takes his food or coffee with him, then he must recite a new Beracha when he resumes eating outside. In this case, his original intention was to eat at home, and he then decided to bring his food outside, and so he must recite a new Beracha. This is the ruling of Hacham Bension Abba Shaul (Israel, 1923-1998), in Or Lesion (vol. 2, p. 105), and of Hacham Ovadia Yosef, as recorded in Yalkut Yosef (p. 94; listen to audio recording for precise citation).
Summary: A person who eats as he walks does not recite a new Beracha each time he takes a bite, because his original intent was to move locations as he eats. Similarly, if one began eating or drinking at home but it was obvious he was planning to take the food or drink with him, such as if one takes coffee with him on the way to work but begins sipping the coffee at home, he does not recite a new Beracha after he leaves the house.
