Weller wrote two articles: one in 1971, which is where the quote came from, and a 3-part series in 1954. In the earlier article he does not say anything about the provenance of the small-bore Enfield, but does have a photo of it alongside 2 Whitworths (one long and one short). The Enfield looks very similar to the "long" Whitworth, except that the forestock does not extend quite so near to the muzzle, and the rear sight is mounted considerably further forward. It appears to have two bands, and the rear sling swivel looks to be attached to the front of the trigger guard.
Earlier in the article Weller states "There was the more conventional .45 caliber Enfield with both Henry and Turner rifling. A very few .44 caliber Kerr rifles also survive. The weapon at the Springfield Museum made by the London Armoury Company, where Kerr was superintendant, is of this type."
So he appears to have been quite familiar with Kerrs, Turner, etc.