The latter, I'm ashamed to say. They do provide dishes on the tables to take them out though! (Well, they had to do something with the ashtrays now smoking's banned...)

You may also be interested in:

http://www.tea.co.uk/guildmembers.php

I can confirm that Moggerhanger Park, near me, does an excellent cuppa, and rather good cakes, in bizarre surroundings (as you'd expect, from somewhere that sounds like a cat storage system).