The general view on the issue of 2-pdr high-explosive (HE) is that there was none, and that the guns were only equipped with armour-piercing (AP) rounds. While sometimes one comes across references to 2-pdr HE (see e.g. at this link), these are vague and from memory, written years after the fact. So you can imagine my surprise when I came across a short statement in the war diary of 11 Royal Horse Artillery (R.H.A. – the famous ‘Honourable Artillery Company’ of the City of London), in which German tank methods and ways of dealing with them are discussed.
15. The 2-pr H.E. has been used most effectively against soft vehicles but it is doubtful if there is much more in the country.
11 R.H.A. was a 25-pdr regiment, but it would have worked closely with 2-pdr equipped AT regiments during January 1942, when the Allied forces were operating in mixed columns. Nevertheless, this report does not pertain to operations during the Axis counter-offensive. The relevant appendix is part of the February 1942 war diary. The report was issued by HQ R.A. 1 Armoured Division on 20 January 1942, so it would be based on experience in fighting up to that date.
The document can be found in Kew, under WO169/4560. I’d be interested in comments on this.
Thanks to user ‘idler’ on WW2talk, here is a link to the 2-pdr equipment page with ammunition production statistics.