hello William .... I've looked through several of the standard books on pressed glass - those which include some discussion on B.T. coloured wares - but regret to say I can't find any specific reference to a name for the red colour of these swans.
The books make common reference to the factory's 'Topaz Opalescent' ware, and makes mention of the fact that a variety of colours were popular with B.T - including black for swans (whether it was black or a very dark purple I've no idea).
Uranium (as can be seen in your centre swan) was popular, and assuming I'm reading the books properly, this uranium colour gave rise to a rare and attractive variety called 'Sunrise' - apparently yellowish shading to pink and then ruby on the edges.
As with other prominent glass producers, much information on new products was published, including novelty inventions, in the 'Pottery Gazette', and somewhere in this publication during the period mid 1880s to 1900 there may well be detailed descriptions of B.T. colours. Another printed source, which I wasn't aware of, was their own 1881 sixty-two page cloth bound catalogue. It's possible though that this date would have been too early to have included all of their novelty colours, especially since 20086 wasn't Registered until 1885.
As for accessing these publications, you might try the V. & A. in London, the British Library or possibly The National Archives at Kew. Of course, others here may well have far better ideas as to sourcing these things.
In 1882 Sowerby created a red glass which they called 'rubine' - a red that appears to shade toward a slightly goldish red depending on how you viewed the piece. I could be very wrong - and am well aware of expert comment that it was only post 1920 that selenium and copper were used to produce pressed glass in red - but am not entirely convinced that Sowerby would have used gold, even in 1882 - especially in the quantities that would have been required for the output of their large pressed bowls in 'rubine'. But as I say I could be wrong and perhaps it really was a gold solution.
Just as a matter of interest, from where did you source the name 'primrose' for your B.T. uranium swan - I'm not doubting the name but don't recall seeing a reference to this in my quick squint at the various entries on specific B.T. colours, although am aware that Davidson used the word to describe their yellow 'Pearline'. Am sure I've almost certainly missed it somewhere.
As you'll know, B.T. copied almost identically some Davidson colours (the Pearline ones in particular) - I think B.T. used the word 'Topaz' instead of 'Pearline', but the similarity is striking to the extent that Colin Lattimore comments... "...the appearance is hardly distinguishable from that of Pearline glass. "One can only assume that some technical detail of manufacture rendered it sufficiently different not to contravene the Patent Law."
Just to add, however, that the uranium swan here is not a 'Pearline' or 'Topaz' verion - it's simply uranium (not re-struck of course).
Sorry this doesn't help remotely with naming the colour of your red swans - but just might help by jogging someone's memory.
Ref. 'English Pressed Glass 1830 - 1900' - Raymond Slack - 1987
'English 19th-Century Press-Moulded Glass - Colin R. Lattimore - 1979.