The Government department that deals with this is the Insolvency Service. Their website indicates they keep records back to 1960, but that's it.
You could try contacting them to enquire, but I'm afraid that I doubt it will be easy .
1923 to 1928 is a wide scope of enquiry - there will have been many some bankrupcies over 5 years.
http://www.insolvency...storicdata/HDmenu.htm