Does anyone happen to know what the commuter trains into London from
Arlesey (i.e. the Peterborough line) are like in the morning? I'm
particularly interested in whether the morning trains are standing room
only by the time they reach Arlesey, as they are from the nearby Letchworth.

At certain times of the day, Arlesey station has an hourly, rather than
half hourly service (every other train runs through without stopping)
and the ticket office is open mornings only. Some of the faster trains
from Letchworth are but the 8.43 from Letchworth starts there and you
can usually get seats then.