From googling it seems its well known that SophosAV as well as other AV programs have issues with how they interact and can inhibit source control utilities like TortoiseHG or TortoiseSVN.

One solution is to exclude directories under source control from on-access scanning as detailed here on Sophos's support site. There is a corollary article that mentions some issues related to this, namely need to place multiple entries for exclusions based on the possibility of the location being accessed through the short vs. long name (e.g., Progra~1 vs. "Program Files").

One other twist is I am using a junction to relocate my user directory, C:\Users\Username, to a second hard drive, E:. Since I am not sure how this interacts I have included the source control directory as they are nested in both locations. As a result, I have included the two exclusions for the on-access scanning exclusions (and to be on the safe side on-demand exclusions as well, although this should only come into play when I select a parent directory of the exclusion to be scanned on-demand, but still). You'll notice I have no need to add extra exclusions for those locations based on short vs. long name distinctions. The two exclusion I have then, for both on-access and on-demand scanning exclusions are:

C:\Users\Username\source-control-directory
E:\source-control-directory

However, this does not seem to work as TortoiseHG still lags terribly in response to any request as AV software starts scanning when the directory is accessed via TortoiseHG.

I can verify without a doubt that Sophos is causing the problems: I can completely disable on-access scanning. Once this is done TortoiseHG responds very fast to all operations. I cannot leave this disabled obviously, but since the exclusion don't seem to be working, what next?