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No, but in the FCC timetable booklet trains operated by 377s are indicated by a pink star at the tops of the columns showing that the train in question has a disabled access toilet.
They're only indicated that way on the weekday timetable. I'll see if they're on UKmodernEMU...
...and they're not. From personal experience though, I think the 1434 from St Pancras is a 377 (and the preceding service from Bedford - probably the 1324).