The recent downward revision of the solar photospheric abundances now leads to severe inconsistencies between the theoretical predictions for the internal structure of the Sun and the results of helioseismology. There have been claims that the solar neon abundance may be underestimated and that an increase in this poorly-known quantity could alleviate (or even completely solve) this problem. Early-type stars in the solar neighbourhood are well-suited to testing this hypothesis because they are the only stellar objects whose absolute neon abundance can be derived from the direct analysis of photospheric lines. Here we present a fully homogeneous NLTE abundance study of the optical Ne I and Ne II lines in a sample of 18 nearby, early B-type stars, which suggests log[epsilon(Ne)]=7.97+/-0.07dex (on the scale in which log[epsilon(H)=12)]) for the present-day neon abundance of the local ISM. Chemical evolution models of the Galaxy only predict a very small enrichment of the nearby interstellar gas in neon over the past 4.6Gyr, implying that our estimate should be representative of the Sun at birth. Although higher by about 35% than the new recommended solar abundance, such a value appears insufficient by itself to restore the past agreement between the solar models and the helioseismological constraints.