This paper describes an instrument for imaging spectroscopy of ultraviolet (UV) line emission from the solar corona, in the 0.3-1.2x102 nm wavelength range. The optical design for this Ultraviolet Spectro-Coronagraph (UVSC) is an externally occulted, off-axis Gregorian telescope where the secondary mirror is a Toroidal Varied Line-Space (TVLS) grating. A field stop with multiple slits is at the prime focus of the telescope’s mirror. This multi-slit field stop is the entrance aperture for the spectrograph. The slits select a number of strips in the field-of-view (FOV) with enough separation to minimize the spectral overlap of the UV lines dispersed by the TVLS grating. This type of gratings allows for a much larger stigmatic FOV (i.e., 3° x 4°) in both the spatial and spectral direction than that of the Toroidal Uniform Line-Space (TULS) gratings. The complete imaging of the FOV is obtained by interpolating the slit images along the spectral dispersion direction. As an example, this paper discusses the possible use of a UVSC instrument on HERSCHEL, a NASA sounding-rocket payload, and on Solar Orbiter (SOLO), an ESA mission. HERSCHEL includes the Sounding CORona Experiment (SCORE) that comprises a UV Coronagraphic Imager (UVCI) for narrow-band (i.e., λ/Δλ≈10) imaging of the HeII, 30.4 nm, line. How a spectroscopic capability (i.e., λ/▵λ ≈0.3-1 x 104) would enhance the HERSCHEL science is discussed. The SOLO mission is planned for launch in 2013. Its orbital profile will bring the spacecraft as close to the Sun as 0.22 A.U. Also SOLO would represent an ideal and unique platform for a compact UVSC instrument (i.e., ≈ 1-m length) capable of obtaining simultaneous imaging and spectroscopy of the UV corona. The expected optical performances are presented for a UVSC/SOLO optimised for the OVI doublet, 103.2/103.7 nm.