I made a couple of phone calls over the last couple of days doing further research on milling kit, trying to suss what might be most appropriate for my needs, which were quite revealing.
Peterson Mills are more robustly built than a Warrior, and meant for harder use going most of the time, not necessarily the right kit for a hobby or small wood owner. They cost something like £15K plus the VAT. There's a 'junior' model, but its not usually carried by Loglogic, the UK importer.
Where I might have made something of a naive logistic boo-boo, is I've watched loads of videos of milling into planks, as shown on Logosol and the Warrior videos. It was probably softwood. However, it seems you can't just cut oak into 1" planks of your desired dimensions and then stack it to dry. It'll warp all over the place. Maybe OK for green Oak furniture but not joinery boards. Apparently what's done with oak is its cut through and through (horizontal sections) into really quite thick long boards, maybe 20ft by 4 inch thick and a couple of feet wide, too heavy to handle manually- it needs a front loader. Then the tree is 'reassembled' horizontally with spacers between the slabs, and left covered to dry slowly for a good couple of years. Only at the end of this when its nearly seasoned, its milled a second time down to the final required board size. As you're dealing with large diameters, its initially got to be done by a bandsaw, a Peterson or warrior couldn't cope with a couple of feet, although they might do for the 'final cut' to board size.
Still got to do quite a bit of footwork and research to fully understand the oak milling process. At least if I've 1/2 ton slabs stacked in the yard, someone nicking them is less of a concern.