The stats I`ve been involved with on v8 models tend to fail "shut", Phil. Then you have the opposite effect!!
XK, 308 and S-type all have similar heating and cooling systems. They are a precision system (Jaguars description) Functioning correctly you should have heat in the cabin in around two minutes. Assuming the XK has an almost identical system to an S-type, remove the header tank cap and watch for a coolant flow from the bypass pipe on the side of the thermostat tower to the tank. That is a good indicator that a coolant flow is present.
The auxiliary electric pump should be checked for functionality. Find the fuse and test for voltage and if possible current flow using a suitable electrical test unit. That pump is quite important around town where idles speeds can slow down water flow though the matrix.
Air locks can be difficult to burp out on the V8 models. Any air in the system affects cabin heating as indeed I have experienced myself. Lift the top plastic engine cover to expose the thermostat tower complete with thermostat housing directly behind the belt driven water pump on the front of the engine. There is a screw cap on the tower with a hex drive socket to unscrew it. Any air removal in the system or topping up is done at this highest point on the engine. Go easy because these old plastic towers embrittle with age. On the front of the tower is the thermostat tower and nozzle with the thermostat behind it. Three bolts secure the front nozzle to internal threaded brass ferules in the tower which can frequently break free and spin making nozzle removal difficult or impossible. Aluminium replacement units are available for as little as about £30. Well worth having one to hand if you need to burrow into the thermostat and water pump.
There was an issue with some of the thermostats in the early V8 models. Again worth changing for the sake of about £12. Don`t be tempted to buy old new stock from a certain supplier on the internet. I made that mistake and instantly boiled an engine......
The biggest issue with the 4 litre V8 cooling system is the water pump itself. Most will have been replaced by now with the pump fitted to later 4.2 engines. Later pumps have six 8mm mounting holes and TWO ADDITIONAL BOLT HEADS visible on the front of the pump. The original pumps had plastic impellers which would frequently break up, reducing pump flow causing overheating and blocking the engine with broken blades. £35 buys you a new metal bladed pump on ebay.
One more item you should consider changing. I had a failure with one of these in front of the whole Forum team at Weston Park a few years ago. The cylinder head temperature sender is mounted in the plastic manifold pipe which links the two heads together at the front of the engine in close proximity to the thermostat tower. This £13 sender when it fails (77k miles in my case) causes the temperature gauge to show full hot even when an engine is cold. It mucks up cold start enrichment and general running parameters also.
Nothing lasts for ever so in the search for your lack of cabin heat and if you have to do some work to correct, you might consider replacing the items above to bring the car up to a known condition. If you have that little lot apart, also bend the serpentine drive belt back on itself and check for across belt cracks. Replace if in that condition. Idler pulleys should also be checked for a dose of the wobbles. Certainly on the S-type, the top idler can flop about. Usually that is down to the centre securing bolt and internal bearing centre piece not being set out far enough when the engine was constructed. Minor adjustment cures that issue.
All this caper is described in these links together with photographs which might make things clearer.
http://www.jec.org.uk/forums/viewtopic.php?f=201&t=5465
http://www.jec.org.uk/forums/viewtopic.php?f=201&t=6228
http://www.jec.org.uk/forums/viewtopic.php?f=201&t=4685
Mike K