For any HN'ers based in London the British Library in St Pancras is a fantastic resource, and their Business and IP Centre ( http://www.bl.uk/bipc/ ) has an easy signup for a Readers Pass for entrepreneurs.
I tried getting some work done there a couple of years ago. All the desks were taken and the internet was a nightmare to get onto and highly restricted. Things may have changed since then. I tried going into the Business centre but lacked the required ID.
I think it's set up to help the people looking at the physical resources they have there (older and rare books on paper mostly), rather than someone looking to work exclusively with an internet connection. If you're not interested in the books, it is of course not a great place to work, though the cafe is pretty good for meetings.
I'm not sure it's really an appropriate place for entrepreneurs unless they are interested in accessing or using the books somehow. When all the other libraries have shut down or turned into Internet access centers, this one will still be valuable as a repository of the books we choose to keep as physical artefacts.
It's not really that kind of library, it's a central store for valuable (or just old) physical objects. They didn't even previously give out membership unless you had a request for a specific title that they hold which wasn't available elsewhere. Accessing all information is not their central purpose, accessing specific information on paper is.
