A similar commute put me off many a school morning. A hurried walk with sleet in my face, carrying heavy bag(s), to then stand with my face in someone's armpit, uncomfortably hot because there'd been no time/space to remove the outer-clothes necessary for the initial walk, followed by the jostling to get off the train before another (admittedly much shorter) walk to school, in what felt like a rapid white water ride of people rushing like a current you move with or drown under, before getting to put down the bag that had been digging into your hot but damp with freezing water's shoulder. Then can you pee before the bell goes or will your morning wee that wasn't quite ready when you left the house at 7.35 have to wait until gone 10.30 to evacuate itself?
Bringing back memories and I sympathise with my teen self, forgiving her for often giving up by Thursday, or at least Friday, skiving under the duvet or at the haven of boyfriend's flat.
And ... all this in the suburbs so similar in London would be a horror I would have to avoid for self-preservation, or know that I'd end up failing through quitting.
Apologies for the horrid sentence structures above- emotive garbled response...
However, if it were a straight 55min drive on mainly clear and straight roads, or a single quiet bus or train journey I would say you were probably BU. As it is, that commute sounds like one I'd avoid for my sanity, as well as confidence, as to attempt that long term would just be setting myself up for failure.
Have you researched all transport routes? If that commute really is the best option then yanbu to avoid that location.