first guess is EGR, look at blocking it, then look at injector seals :)
also may be worth removing top hoze from intercooler incase one is collapsing restricting air flow, = not enough air to burn fuel and smoke
i'm pretty sure the white smoke will be un-burned fuel, does this clear once started and warmed up? though another cause is a stuck EGR, injectors may be leaking air past, or could be general compression issue,
my first call would be injector test followed by compression
lubrication :)
aside from that, check if the recall work's been done
https://www.lro.com/blog/news/land-rover/1509/faulty-tow-bars-mean-major-land-rover-recall
if you checked oil just after a run it will be lower then after standing due to the oil circulating around the engine so standing = higher reading then just after running
or if your really worried
http://www.theoillab.co.uk/product-category/oil-testing/engine/
i did not have it on a disco unfortunatly only had a renaxxxx at the time, there is an adapter for the thule velo compact
https://www.thule.com/en-gb/gb/bike-rack/towbar-bike-racks/thule-velocompact-927-_-927
+...
https://www.thule.com/en-gb/gb/bike-rack/towbar-bike-racks/thule-rideon-9503-_-9503
that's the one i used to have, sturdy, but heavy and bulky, and due to how the door opens on the disco dont think you can get in to boot without bike removal
something like this...
http://www.discovery2.co.uk/waterpump.html
ther's info on a drin plug there :)
does say plug can be stuck and require bottom hose removal fingers crossed for you :)
the one u r hoping to look at last MOT was a pass, but as per mot history checker ""The rear chassis section is in an advanced state of corrosion""
also prev mot's seem to have mention of lot's of iron oxide too :(
http://prntscr.com/ezzr5l
if it's the same as the above pic taken from FB, the bellhousing is not an oil filled item, ergo there is no gasket between the housing and the box, listen to @jamesmartin he is the gearbox guru :)
water wont give adequate lubrication, diesel/ heating oil very thin, gearbox etc too thick so chance of heat build up in pump mech causing combustion i'd immagine
also check that diesel getting to engine at pressure, friend was working on a disco and one of the pipes inside the pump had come loose, diesel was still flowing just not at a high enough preassure to do anything... :)