The early Northern Fleet lacked operational depth

Could the early Soviet Northern Fleet have challenged Britain or Norway?

No; poor readiness and limited officer experience left it weak enough that even Norway probably held an advantage.

The 1930s Northern Fleet was far weaker than its nominal inventory suggested, and even Norway's navy probably could have defeated it. Norwegian ships were more consistently operational, and their officers generally possessed more experience at sea. Repeated Soviet leadership losses reduced readiness further. Paper strength and national reputation can obscure how much naval power is actually deployable.