  In this paper we present the results of the first low frequency all-sky
search of continuous gravitational wave signals conducted on Virgo VSR2 and
VSR4 data. The search covered the full sky, a frequency range between 20 Hz and
128 Hz with a range of spin-down between $-1.0 \times 10^{-10}$ Hz/s and $+1.5
\times 10^{-11}$ Hz/s, and was based on a hierarchical approach. The starting
point was a set of short Fast Fourier Transforms (FFT), of length 8192 seconds,
built from the calibrated strain data. Aggressive data cleaning, both in the
time and frequency domains, has been done in order to remove, as much as
possible, the effect of disturbances of instrumental origin. On each dataset a
number of candidates has been selected, using the FrequencyHough transform in
an incoherent step. Only coincident candidates among VSR2 and VSR4 have been
examined in order to strongly reduce the false alarm probability, and the most
significant candidates have been selected. Selected candidates have been
subject to a follow-up by constructing a new set of longer FFTs followed by a
further incoherent analysis, still based on the FrequencyHough transform. No
evidence for continuous gravitational wave signals was found, therefore we have
set a population-based joint VSR2-VSR4 90$\%$ confidence level upper limit on
the dimensionless gravitational wave strain in the frequency range between 20
Hz and 128 Hz. This is the first all-sky search for continuous gravitational
waves conducted, on data of ground-based interferometric detectors, at
frequencies below 50 Hz. We set upper limits in the range between about
$10^{-24}$ and $2\times 10^{-23}$ at most frequencies. Our upper limits on
signal strain show an improvement of up to a factor of $\sim$2 with respect to
the results of previous all-sky searches at frequencies below $80~\mathrm{Hz}$.
