A bit more input on this, the starting problems are getting worse, though it's always OK when the engine is hot.
And the hesitation is still there at times, randomly unpredicatable as ever.
Today I asked a retired garage-owner friend of mine to observe a cold start after 2 days of non-use.

I just cranked it until it fired, which was a few seconds and very rough. After a few more seconds of idling it was running normally.
He was at the rear and said there was nothing unusual in the exhaust except a bit of unburnt fuel as expected.

Hi thoughts are maybe it just needs a new fuel filter, I have no record of it ever being done. 80,000 miles (nearly, service due soon!) and all Audi "long-life" servicing so far - would they ever change it?

Any other thoughts?

I change my fuel filter every two years. Do it myself. Buy filter and crusher gaskets and just change it. I can help you.

Fuel filter change is not in service schedule for petrol engines so it's probably have never been changed.

Is it maybe loosing fuel pressure, leaking air in fuel system when parked for prolonged periods of time. Or leaking injector slowly letting fuel in manifold which builds up while stationary and causes mixture to be too rich at startup until it vents out.

Or possibly one of temperature sensors is giving wrong readings.

Well as a first step I've just swapped the MAF back to the original and will see what difference, if any, that makes.

None. :(

Tried starting just now after sitting overnight unused.
Based on yesterdays experiences I pushed the throttle down a fair bit before starting.
It fired up quite quickly, but was very rough (definitely not all cylinders firing) and there was a strong smell of unburnt fuel. Settled down to normal after about 20-30 seconds of keeping the revs up around 1500-2000.

So possibly too much fuel or not enough air or both, but how to narrow down the cause? Or an ignition problem that goes away after a few seconds - maybe not?

While changing the MAF yesterday I had a good look round the air inlet, pipes, filter etc. up to the manifold and nothing appeared amiss. :Confused:

Are your manifold flaps operating correctly on startup?

I haven't checked them for a little while, but they certainly were OK last time I looked and all components appeared to be in top-notch condition, free to move and moving as they should.
A job for tomorrow I guess, but wouldn't they be in the low-rev position at the start, or does that require the bellows to move them - I can't recall which way round the actuation process works.
Could them being in the wrong position (whatever that is) cause this, if so how?

Edit: Just been having a read how this works.
Engine off the flaps are open, giving the shortest inlet (suitable only for high revs)
On starting the vacuum moves both actuators, closing both flaps and giving the longest inlet, suitable for low revs.
So if I had a vacuum leak there could, as they say, be "unexpected results" due to an inappropriate inlet manifold configuration.
I've read a fair few articles/postings about replacing the vacuum pipes with more robust ones.

Yes they are, I just popped out to check.
Took the engine cover off and moved them by hand, all seemed fine (though could they be broken inside?) with both bellows "relaxed".
Started the car, it just caught and "chugged" so I ran round to the front and both bellows had "sucked in" as expected and moved the arms.

Watched it for about a minute by which time it was ticking over smoothly.

Hmm ok well always good to check. I do think its worth changing the fuel filter as Ainars suggested to eliminate that possibility as they are not a huge cost. I've changed mine a couple of times since I owned the car. Sounds like the mixture is not right somewhere in the scheme of things so either fuel system or air breathers etc are main suspects Andrew