I'm open to correction from others on this one, but all 4T rifles of BSA Shirley origin that I have seen that have not been FTR'ed have had Singer manufactured sights. Earlier rifles bear sights marked with Singer's early marking form of SM followed by the last two digits of the date, eg. SM41, & later rifles such as 44 & 45's bear sights with the later allotted code for Singer, of N67 (Northern Area factory number 67). Having said that there are some exceptions in that some rifles were sent to Holland & Holland with battle sights fitted, but which were otherwise up to conversion standards, & these had sights fitted from a stockpile of spares held by H&H. It is known that many rifles were fitted with sights of Savage manufacture. I have seen or owned several, & all were of BSA 1943 manufacture, but other dates may well exist.
Of course, if a rifle has been through ordnance repair or refurbishment it could have a sight of any provenance on it. As Peter has said on many occasions armourers simply fitted what functioned correctly & were not too bothered about the factory of origin.
Hope this helps.