377/1 is confirmed in the Southeastern franchise agreement377s to Southeastern has definitely made it into a franchise spec, but the variant of 377 to be used has never been officially confirmed. 377/1 is a fairly reasonable supposition, that's all.
The Franchisee shall negotiate and enter into an agreement with the TSGN Operator for the subleasing by the Franchisee from the TSGN Operator of [redacted] x 4 car Class 377/1 units ("Additional Class 377 Units") (not being the dual voltage units forming part of the train fleet of the TSGN Operator) (the Class 377 Sub-Lease").