Like many things which appear simple at first glance, reality appears somewhat more complicated.
'Allinson' is a brand name owned by Allied Bakeries, in turn owned by Associated British Foods.
Not to be confused (sic) with Allinson Flour, a separate company, which give, the impression of a 'smallish', high quality, craft bakers.
http://www.allinsonflour.co.uk/As a brand, Allinson Flour is strongly marketed by
https://www.bryt.co.uk/recent-work/allinson/ However, it owned by Sliverspoon, of beet sugar fame, which, in turn is I believe, totally owned British Sugar plc, in turn, totally owned by by the multi-million, multi-national conglomerate, Associated British Foods.
So, in short, Allinson Bread is not associated commercially with Allinson yeast.
Allinson Yeast is simply a a brand name owned by the same multi=national conglomerate as Allied Bakers.
So we've come full circle.