Plants in the post

Legally yes, though there are restrictions or guidance on packing.
https://www.postoffice.co.uk/mail/what-can-i-send

But I'm not sure how well they would travel - it will depend on their size, the likelihood of someone at the office packing them up properly, whether you had breakable pots for them, whether the compost will move around, whether a stem is likely to break etc. etc.