habusaru said:Hello,
Many months later - I want to post a happy update - the seedlings made it!
I gave them as much sunlight as possible (including a grow lamp for when it was frosty outside) and I've had a 7ft wall covered in sweet-pea flowers since June. They've just opened another wave of flowers, so hopefully I might keep them until September.
So - many thanks for the advice and I'll definitely give winter sowing a go next year.
(As well as saying thanks, I wanted to post this result in case other new sweetpea gardeners who were discouraged about their own seedlings saw it. The seed varieties were "captain of the blues" from kitchen garden seeds, plus a few hardy varieties from Ace hardware)