The Mishna in Masechet Shabbat (9b) establishes a prohibition against sitting down to a meal shortly before the time for reciting the Minha prayer. The Gemara discusses this Halacha and concludes that it refers to Minha Gedola, that is, the earliest period for reciting Minha, which begins 6.5 hours into the day. As such, it is forbidden to sit down to a meal from the point of six hours into the day until one recites Minha. For example, if the earliest time for Minha is 12:30 PM, one should not eat a meal after 12:00 until he first recites Minha.
The Gemara further notes that this Halacha applies even to an ordinary-sized meal, provided that it consists of bread. Even an ordinary meal, such as a sandwich, would be forbidden once the time for Minha arrives.
The question thus arises as to when a person should eat lunch. As the Gemara forbids eating a regular meal even early in the afternoon before reciting Minha, it would appear that it is forbidden to eat lunch until one recites Minha. Indeed, the practice in most Kollelim is to recite Minha early in the afternoon, before lunch, in accordance with the Gemara's conclusion. Hacham Ovadia Yosef in fact rules that it is preferable for all people to follow this practice, and recite Minha before eating lunch. This is also the ruling of Hacham Ben Sion Abba Shaul (Israel, 1923-1998), in his work Or Le'sion.
Nevertheless, Hacham Ovadia writes, those who pray Minha at a regular time each day, or have people who will remind them to recite Minha, and on this basis eat lunch before reciting Minha, have authorities on whom to rely. Even though it is preferable to recite Minha before eating lunch, a person may be lenient if he includes Minha in his regular routine or has people to remind him so that he does not forget to recite Minha.
Summary: One should preferably not eat a meal with bread for lunch until he recites Minha, though one may be lenient if he regularly recites Minha at a set time each day or has people to remind him to pray Minha.