Well, I found something weird yesterday. The journey from Hampstead
Heath to Whitechapel is shown by the Single Fare Finder as costing £1,
so evidently is not regarded as a via Zone 1 journey. I don't know if
that's because the expected route is via Stratford then Central and
District Lines, or if it's anticipating the extended East London Line.
Anyway, this is a convenient replacement for my most usual tube journey
(Belsize Park to Aldgate or Aldgate East), it's half the price, and as
an added benefit it allows me to avoid the nightmare of the Northern
Line, so I thought I should give it a try.

I decided out of curiosity to go via West Hampstead. I thought this
would be an interesting experiment because I would have to touch out and
touch in at West Hampstead, so the system would know I had taken the
Jubilee Line from West Hampstead and therefore had travelled through
zone 1. When I touched out at West Hampstead Overground the gate showed
a £1 charge, which would be correct for terminating the journey there.
I crossed the road to the Jubilee Line station, touched in again and
travelled on to Whitechapel. At the Oyster gate there it again showed
£1, which judging by the remaining balance was the same £1. It worked!

On the way home I decided again to travel via West Hampstead. Touching
out at West Hampstead Jubilee Line, the gate showed a charge of £2 -
correct if terminating there. Now, I thought, this feels strange - by
travelling on from West Hampstead to Hampstead Heath it's going to
refund me £1. But it didn't. The gate at Hampstead Heath also showed a
charge of £2 for the completed journey, which I confirmed today on the
journey log. I thought maybe it would apply a refund overnight, but it
didn't do that either.

So, the system can make different charges depending on which direction
you travel. It just doesn't make sense to me. And apart from the
directional assymetry, £2 simply can't be a correct charge from a Zone 2
station to a Zone 3 - it should be either £1 or £2.50. I can't believe
the anomaly is intentional, and I wonder if they're aware of it.