Halas & Batchelor went to war at the bequest of Jack Beddington, a remarkable character who had been Shell's publicity director in the 1930s. Joy described him as one of their best clients, so when he was chosen to become the director of the Ministry of Information in 1940, they were called up to produce cartoon after cartoon to promote the British government's messages throughout the war.
An advert from the March-April 1946 edition of the Documentary Newsletter puts the number at "over 42" and lists some of the artists involved (a post is coming soon on some of them...).
The truth is that we don't know how many films they made, and it depends how you count. Is Handling Ships (1944/5) one long film or seven short ones? Do you count a section of animated diagrams within an otherwise live action film? And most of the resulting films, if they survive, are uncredited. Whatever the actual number, anywhere in the region of 42 animated films - produced in 48 months with a skeleton crew, whilst being moved around London and its suburbs to escape the blitz, dealing with your flat being bombed and the resulting injuries... - is a remarkable record.
Some of these 42+ like Dustbin Parade (1942) have had some profile and been made available online - but less well known is that others are online anonymously as part of the British Pathé channel on YouTube. Issues of Documentary Newsletter available on the Internet Archive include listings of films commissioned by the MOI throughout the war period, and so with a bit of cross referencing I think the films below can all be confirmed as H&B produced films (with one exception at the bottom).
First up is Model Sorter (1943), which has clear shades of Dustbin Parade, but it is notable that other than the very chatty bin, the assorted waste is anthropomorphised and given character without the addition of faces - a trickier skill. The dancing knotted rag is particularly successful.
Early Digging (1943) is a neat piece of work with a song commentary performed by Arthur Young. The characterisation of Jack Frost is perhaps more reminiscent of John's design than Joy's? He has something of the air of the Music teacher in Music Man (1938).
Compost Heaps For Feeding (1943/4) features an animated cartoon caricature of Cecil Henry Middleton Britain's first television and radio gardener, and a familiar voice if not face to audiences of the time.
Cinderagella, or Rags to Stitches (1944) shows that the unit was already well into its stride. In 90 seconds this short filmlet brings a concise narrative, humour, character, elegance, and a convincing propaganda message, and still has time to wrap it all up with a curtain call ending.
The economy of design in Cold Comfort (1944) is perhaps a little too parsimonious, suggesting that it may have been produced in a great hurry or with a shortage of means. It still succeeds with a witty ending and clever character design of the radio.
Blitz on Bugs (1944) is another accomplished work, with much more scale and detail than the previous example. Rather than the fantasy of Jack Frost or Cinderagella, this film has much more of a sense of the sounds and realities of life at war - with the blitz all too familiar to the staff of this London based studio.
In contrast to Blitz on Bugs, in Mrs Sew & Sew (1944) the war seems a world away - except for the resulting rationing. The film is more reminiscent of Joy's character design, familiar from her pre-war illustrastions all the way through to Ruddigore and beyond.
Lastly we come to a film which was apparently not made by H&B, but bears many of it hallmarks. Bones, Bones, Bones - Save Bones (1944) is credited in the Documentary Newsletter to Henry Elwis, who I believe was German (possibly Elweiss originally) and made a semi-abstract animation called The Composer's Dream in 1936. Denis Gifford also credits him as working on a film called How the Motor Works (1936) by British Animated Films - which was the company that is also credited on John Halas' Music Man.
The relationship between H&B and Elwis is a mystery I haven't gotten to the bottom of, but the similarity of the design of the bone characters in this short and those in Dustbin Parade certainly suggest that it is an area worthy of further investigation.
Note - apologies for all the adverts you have to click through on YouTube to watch these. Hopefully you will only get a couple.