There are quite a few places for the V8/P38 to leak coolant..
#1 The heater matrix O rings are an issue with all p38's this will soak the carpet with OAT, chances are you'll smell it and feel it, the carpet gets sodden..
#2 The front cover can leak, along with the waterpump
#3 Headgaskets
#4 Valley Gasket
It is imperative to get it up to temp, take it for a nice long test drive, when you return lift the bonnet and listen to the motor, it should be whisper quiet..
The Rover V8 can have a tick attributed to a good few issues.
#1 Tappets, usually crap which blocks the oil feed hole and NRV in the tappet the easy way to know whether it is tappets or liners, is the tappet will particularly be audible from cold start and continue until hot, if bad..
Another issue is the tappets and cam themselves are worn and can no longer take up the slack..
#2 cylinder liners can slip in the block, this noise ONLY manifests when hot, due to a design flaw in the casting the water jackets are offset in the block and the coolant galley sidewall is quite thin towards some bores and can crack if overheated, this causes the aluminium block to shrink away from the steel liner, and you get a very audible "clack clack clack" noise when hot, this the the liner moving with the piston..
#3 Worn timing chain, which again makes a tap noise,
"cooling system"
The p38's cooling system is marginal at best,
Worn Viscous fans and knackered water pumps plus clogged rads are but a few of the issues that can plague the P38..
The Rover V8 is an all aluminium V8 and it is all too tempting when having leaks to fill it with just plain water, which over time will cause the block to corrode, which blocks the rad with silt and causes the engine to run hot, which exaggerates the liner issue
The VC in the fan can also cause issue, give it a spin with you hand when cold, it shouldn't spin like a top, it should turn but not freely.
There is a documented "newspaper method" but i doubt the owner would let you shred a news paper with his fan
Water pumps can also fail, the indicator is (1) a pretty evident noise (2) a leak from the weep hole on the bottom of the pump, this indicates water has got past the grease seals on the bearing and its ****ed. to be frank
The Front cover can also leak, this usually can be rectified when the water pump is done, an involved job as the sump has to be dropped, but not too bad..
Next up in the Valvetrain..
The V8 is a quick beast, not so much in standing 0-60 but the mid range pull should be pretty good for something with 407nm all available at 2400rpm if it is sluggish expect the cam to be worn, which is common on neglected engines this is usually accompanied with the valve-train tap from above
More to add on that front if required..
AUTO BOX..
The 4.6 is fitted with the ZF4hp24 the shifts should be almost unnoticeable if the gearbox has a shunt or slurrs between gears, expect neglected oil changes to be to blame..
under light acceleration it should change at around 1700rpm, make sure sport works too!!
Check Low range works too, as this is seldom used, the grease in the servo motor turns to concrete and stops the motor working..
Regarding transmissions, the transferbox VCU can seize which causes the front wheels to skip on tight turns try and do some tight turns in a carpark and make sure the front wheels don't skip..
Also on that note..
Check the tyres, they should be a matched set, tread patterns most important as dissimilar treads will cause the VCU to burn out..
The VCU detects a "really" rather than "quite" difference in wheel rotation and grip...
Also listen out of a "chirrup" sound coming from the passengers footwell on overrun this is a sigh the morse chain in the transfer box is slapping the casing and will eventually cause it to snap, with bad results.
especially prevalent on badly maintained or abused examples..
"brakes"
Check the brake fluid, colour should be clear, if it is black that is a sign seals are breaking down..
When the ignition is cycled a Humm should come from under the bonnet, this is the pump pressurising the accumulator, this should stop after 10secs if it continues for a good while then you either have a leak or the accumulator is shot..
Latter is more common..
Worth noting the brake fluid level too, it should be on the full mark or above after standing, if it drops significantly after the pump primes, this is a sign the accumulator has worn. the gas has escaped the accumulator sphere and the space it used to occupy is being taken up by the brake fluid, the butyl seal in the sphere usually fails..
More to come when i can think!