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That's my experience, reservations are most needed in London but less of an issue elsewhere.
Last year I just got on a train from Gloucester to London after I'd DNFd an event. There were not meant to be bike spaces free but, in practice there was at least one free and I had no issues.
I went to the bike at stops to make sure, so I could take mine out, or even get off if need be, but it was fine.I went to Bristol last week and I had a reservation, but didn't need to show it to get on the train at Paddington, and there were several free spaces.
Gwr trains seen to have more spaces than they used to.
On GWR your success depends on whether you can get to the train without encountering an odious member of staff.
At Paddington you definitely want a reservation, at smaller stations or stations with lots of non-reservation trains you’ll probably be ok.