We show herein that the population of star-forming galaxies in the Bremer Deep Field (BDF) has enough ionizing power to form two large ionized bubbles that could be in the process of merging into a large one with a volume of 14 000 cMpc3. The sources identified in the BDF have been completed with a set of expected low-luminosity sources at z ∼ 7. We have estimated the number of ionizing photons per second produced by the different star-forming galaxies in the BDF. This number has been compared with the number that would be required to ionize the bubbles around the two overdense regions. We have used, as reference, ionizing emissivities derived from the AMIGA (Analytic Model of Intergalactic-medium and Galaxies) cosmological evolutionary model. We find that even using the most conservative estimates, with a Lyman continuum escape fraction of 10 ${{\ \rm per\ cent}}$ , the two regions we have defined within the BDF would be reionized. Assuming more realistic estimates of the ionizing photon production efficiency, both bubbles would be in the process of merging into a large reionized bubble, such as those that through percolation completed the reionization of the Universe by z = 6. The rather small values of the escape fraction required to reionize the BDF are compatible with the low fraction of faint Ly α emitters identified in the BDF. Finally, we confirm that the low-luminosity sources represent indeed the main contributors to the BDF ionizing photon production.