Agree that it's the fuel pump relay 2 on a 2001 car, although P1646 did play musical chairs for a couple of years...

Not quite the same car, but the TB on mine behaves as you describe.

@Jay, if you look at the DTC lists 1998 to 2001 you will see the variations. finally settling as the HO2 sensor for the 4.2

 

Hi Mike.

Yes, the TB on my car moves around and makes some adjustments with waking up with key...

Yeah, I'm don't want to send the OP in the wrong direction or give misinformation (if I haven't already) but I was pretty sure that the p1646 was to do with either O2 sensors or fuel pump issues...

I was just thinking of you Mike. In the Excel graph the OP put up, I am not used to O2 sensor readings being displayed this way, in the 4 O2 sensor rows,,, do the O2 sensor values reported look "normal" or LOW for a cold to warmish car? To me they looked off, at second look.

 

I will "re-do" the numbers now I have two working pumps As I'm not convinced the original problem will have gone away

 

Just a quick update - We decided (or I convinced Mrs Joker) that it would be fine to take the XK away for a few days.
Drove down to Lyme Regis and back with no issues, no starting problems at all. That suggests changing the relay fixed the problem which is interesting as I (wrongly it appears) thought that the second fuel pump relay only engaged the pump for additional fuel to support the S/C.

As an aside I've actually changed both relays as I originally borrowed the heated rear window one to test with.

Hopefully that is now something ticked off the list

 

I believe that the second pump does the initial priming of the fuel lines at key on, so an intermittent fault there could definitely affect starting. The designers obviously hoped this would be enough exercise to keep both pumps in working order. A better design would have been for the two pumps to completely swap roles at each key on, but maybe there simply wasn't enough memory left in the 1990s era ECM to add that functionality.

 

That’s very interesting and of course explains everything perfectly.
strangely, when I embarked on the journey to track down the starting problem - the first fault found was a dead secondary fuel pump - tested by removing and bypassing the relay, I wasn’t getting any codes thrown so had no clues the relay was dead/failing

 

Exactly what the ECM does when it detects a relay fault on the fuel pumps is anybody's guess, but it certainly explains the problems you had. BTW I just checked my live MAF reading and it comes out very similar to yours - so either both our cars have a faulty MAF, or they are both working as intended.