Since buying my table and track saw I’ve learned not to regard the factory edges as straight or square but to cut them myself, also to cut in a few mm to get a clean edge.
I would refuse the delivery of badly marked faces on MDF or proper birch plywood, anyone that does proper B / BB grade birch ply expects this too and takes some care with the goods.
I use S L Hardwood in Croydon, they are a proper timber merchant selling to people making things out of wood, unlike Wickes who are selling particle board and joists to builders primarily.
As for “straight” planed timber, hmm, S.L. Hardwoods are OK, because they actually care but Alsford, Wickes etc. I take a square with me and only pick stuff that’s actually square and straight enough along the length to be useful. Be aware that most of the timber from these suppliers has been fast dried in a kiln and then shipped and is likely much wetter than it’s final furniture state and has much warping left to do.