This is the initial paper in a series presenting the first optical detections and subsequent follow-up spectroscopy of known southern Galactic supernova remnants (SNRs) previously discovered in the radio. These new detections come from the Anglo-Australian Observatory (AAO)/United Kingdom Schmidt Telescope Hα survey of the southern Galactic plane which has opened up fresh opportunities to study Galactic remnants. Here, we present the first optical imaging and follow-up spectra of Galactic SNR G279.0+1.1 where a series of 14 small-scale fragmented groups of Hα filaments have been discovered in a area centred on G279.0+1.1. Individually they are somewhat inconspicuous but collectively they are completely enclosed within the overall radio contours of this known SNR. Three of these filamentary groupings are particularly prominent and optical spectra have been obtained across two of them. Their morphological structure and spectral characteristics are typical of optically detected SNR filaments. A very strong [Sii] emission relative to Hα has been detected with [Sii]/Hα > 0.7 and 1.1, confirming strong, shock-heated emission. This is sufficient to classify these filaments in the likely SNR domain and therefore indicating a direct connection with the radio remnant. Other typical SNR emission lines such as [Oii] at 3727Å, Hβ, [Oiii] at 4959 and 5007Å, Hα and [Nii] at 6548 and 6584Å were also detected, lending strong support to an SNR origin of these optical filaments. The value and insights that these optical data can provide for known remnants are discussed along with their relevance to the Galactic nitrogen abundance. A serendipitous discovery of an adjacent Hii region is also briefly described.