As it is known that one is not allowed to eat before morning prayers, is there any opinion that allows to eat after birkot hashakhar but before tefillah?
Shulchan Aruch 89:4: "One who is thirsty and one who is hungry - behold they are in the category of the ill. If one has the ability to focus one's mind, one should pray. If not, if one wishes, one should not pray until eating or drinking."
Rambam's Mishneh Torah, Prayer 5:2: "...if he can concentrate, he recites the prayer; if not, he should not pray until he has eaten and drunk."
From the above it appears that if one is very hungry he must eat before praying according to the Rambam. Beit Yosef 89:7 takes it down a notch and says that eating is optional and subject to one's discretion - "הרשות בידן." Mishnah Berurah 89:26 agrees with this conclusion even in light of the fact that today we are not able to concentrate during prayer even when not hungry.
אם אין ברירה אחרת ולא תוכל להתפלל ולקרוא קריאת שמע לפני העבודה - אפשר להקל ולאכול עוגה קטנה ולשתות איתה כוס קפה או תה חם, אחרי ברכות השחר
If you have no other choice and can not pray and recite Shema before work - one can be lenient and eat a small cake and drink a cup of coffee or hot tea after the morning blessings