I'm afraid I know nothing about the Harrisons; looking at my old election results, they certainly did not seek election to the Town Council as other builders, such as the Adeys, did.
At the end of 2015 I downloaded a report on a proposed Conservation Area. It has very useful text, maps and photos of the area's development. This is what it says about the Harrisons:
"No. 19 [Craven Road] has its own ‘roof line’, and is followed by houses Nos 21/23, which give the appearance of semis built into the street terrace. It is probable that these were built one at a time, perhaps by different builders. Documents show that in 1861 John Shaw [who had Westfields Farm] sold land to builders Joseph and Edward Harrison of Bartholomew Street, and they probably built Nos 21/23."
Despite searching yesterday, I've been unable to find where I got the report from! However, it's headed " Newbury Town Council - Conservation of Historic Buildings Working Group 30.3.2009 - Report on Proposed Westfields Conservation Area". Perhaps you might have more luck searching online, or approach the Town Council. It is certainly worth getting a copy.
Bedford Place became Maidenhead House before 1966 according to an old map I looked at.
https://www.old-maps.co.uk/#/Map/447059/167759/13/101329 (zoom out to get the free view, and scroll south).
In the early 1960s, local artist Christopher Hall took photographs of the old courts and yards, and I think these are now with Newbury Museum; they may have a view of Bedford Place prior to demolition.