Alan,
   Congratulations on the re-purchase of the XJ40.  Great car!!
Since you are aware of the amount of the drain on the system, you need to
isolate which circuit it is on.  Once you have done that -- it is pretty
simple to determine which appliance is causing the drain.
   Your radio must not be a standard for '88 -- at least not in the US.  My
original '88 Radio had no codes by which to activate it once the power was
off.  It is a simple matter of re-setting the stations that I frequently
listen too.  I do know that on later models, the security codes for the
radios were placed on a label on the inside of the bonnet.  That way they
were always available.  If worse comes to worse, you can contact Jaguar and
they can get you the codes -- providing it is the radio that came with the
car!!
  To understand this properly on the puddle lamp -- you are saying that the
bulb shows continuity and the sockets the bulb clips into show 12 volts but
when you put the bulb into the clips it does not work??  Try swapping bulbs
with one that you knows works.  This is not a matter of the computer if you
are getting 12 volts to the clip.
   The bulb warning light can be any number of problems.  The puddle lamp
is not the cause since it is on a totally different circuit and does not
send a bulb out warning to the dash.  The first thing you need to do is
check all the bulbs.  This means directional as well as the brake lights
(with your foot on the pedal)  to make sure they are not the cause as well
as high beam.  Usually on the directional, the warning comes on when you
activate them -- but not always.  I suggest you check to make sure all is
working as it should.  If you still get the warning than you need to go
around the car with a wire plumbing brush and clean all the sockets. Clean
the base of the bulbs as well.  If that doesn't work then you need to
re-solder the Bulb Failure modules-starting in the boot.  These cars are
notorious for bad solder joints and will cause warning all the time.
   I have had the car go dead in the middle of traffic  -- but not over a 3
year period of time.  Mine lasted about 3 weeks.  I changed out the
Crankshaft Position Sensor on the front of the engine and I have never had a
problem since.  These items, again, are a common and notorious source of
anguish and if you haven't changed yours out -- you will!!

Webserve
'88 XJ40  with 205,000 miles  (330000 km)

As for the cutting out, I had a problem with my 92 Sovereign that was
similar.  Turned out to be the connector on the fuel pump harness in the
trunk.  I just cut out the connector, replaced it with crimped splice
connectors, and haven't gotten stuck in 2 years (knock on wood).  Diagnosis
of this problem involved 'jiggling' the harness around in the trunk until
the fuel pump cut out.

Light bulb getting 12+, yet bulb not lighting?  Did you measure continuity
with the bulb removed from the clips or in situ?  Either way, sounds like a
bad bulb, maybe shorted internally.

Good luck.