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The Thameslink site covers it pretty poorly:
https://www.thameslinkrailway.com/travel-information/on-board/bringing-a-bikeThere aren't any mentions of restrictions leaving London outside evening peak. But the more you read it the less sense it makes for other times...
trains travelling away from London that are timed to depart from or pass through any central London station between 16:00 and19:00 Monday to Friday, except on public holidays
what does 'a train travelling away from London' mean when many of the trains go from Sussex right across London, with about 20 stops inside it, and then to Hertfordshire?
which stations are 'central London'?
Anyway, should be fine for your journey.
has anyone got away with putting a bike on one of the trains out of city thames link during the morning aprrox 8am? I get why they ban bikes coming in but surely there's room for a bike leaving london? i need to get to stevenage