Zipcar followed by a rental for your long journeys.
Being realistic even at 36 as a new driver your yr 1 (and probably yr2) insurance will be absolutely insane. Especially if you're parking on the street in London.
If you're happy to lease, get whatever deal you can wrangle the 1st years insurance bundled in.
Otherwise I'd see any car as a 2yr stop gap with the cheapest insurance possible until you can get something you like once your premiums come down.
From this list a Polo seems a good shout.
Another left field option is to get some sort of old saloon or estate which qualifies for classic car insurance - given you expect your mileage to be low. This is on the basis that from your brief 99% will be either motorway driving or stuck on one of the London ring roads. It means you could get away with a larger engine which will make motorways more pleasant - otherwise it's hard to square the circle of a small engine which in a big car will be underpowered, or a small car that will be too small for IKEA...that's why the Jazz always gets suggested.
Also on your OH doing her test, probably best that she does a manual test so she at least has the option of driving a manual, if say for eg you go somewhere where you can't rent an auto. Also driving a manual isn't much harder to learn. The challenge of learning is having to coordinate a whole new set of physical and mental skills all at once - moving the gear lever and clutch obviously adds to that, but it doesn't remove all the other elements.