The ages of the oldest and most metal-poor stars in the Milky Way bear important information on the age of the Universe and its standard model. We analyze a sample of 28 extremely metal-poor field stars in the solar vicinity culled from the literature and carefully determine their ages. To this aim, we critically make use of Gaia data to derive their distances and associated uncertainties. Particular attention has been paid to the estimate of the reddening and its effect on the derivation of stellar ages. We employed different reddenings and super-impose isochrones from different sources in the stars color-magnitude diagram built up with different photometric systems. We highlight subtle metallicity effects when using the Johnson photometry for low metallicity stars and finally adopt Gaia photometry. An automatic fitting method is devised to assign ages to each individual star taking into account the uncertainties in the input parameters. The mean age of the sample turns out to be $13.9 \pm 0.5$ Gyr using Padova isochrones, and $13.7 \pm 0.4$ Gyr using BASTI isochrones. We found also a group of very metal-poor stars ($\left[\frac{Fe}{H}\right]$: -2.7 -2.0 dex) with relatively young ages, in the range 8 --10 Gyr.