What I found out was largely as follows:

The hotel I was staying in advertised itself as having free wifi on the ground floor. It did, but the signal was no greater than 40%, and as I was on the 7th floor I had to come down to the bar to use it. This was fine, and I used this for my morning and evening email sessions.

There are lots of University buildings in London, some of whom subscribe to the JANET Roaming Service. As I’m a member of a participating University I can use their networks for free. This got me a connection on floor 7 of the hotel twice, and would have been an option in a couple of other places as well.

The rest of the time I generally used The Cloud, mostly in or around Pret A Manger stores. It’s possible to get free wifi in a fair few places (largely pubs and cafes), and my most productive session of the whole trip was the last hour outside Euston station where I got through all my home and work email with a near 100% signal.

So yes, I managed to stay up to date, and maintained Inbox Zero throughout the trip.