It worked! (sort of)  The dull tasks I tackled last week in hopes of gaining inspiration didn't produce any flashes of genius, but they were useful in themselves, and I felt virtuous enough afterwards to grant myself leave to sit in the garden a while and read.
The book I chose was one I first read many years ago, What Do I Really Want? by Lloyd Lalande (Harper Collins, 1995).  It was interesting to find out whether I felt the same way about the book after such a long period.  I have to say that I'm rather more sceptical now than I was before, but the part on trusting your intuition really bore fruit.

"One way to tap into your intuition is to ask yourself questions without looking for an immediate answer. Instead, wait for the answer to come through your intuition.  When I set a goal, I often ask myself what it is I need to know to guarantee reaching it.  Sometimes it takes a few hours for an intuitive answer to come to me; on other occasions it takes a day or even a week.  I have learnt to trust my intuition, and the answer always comes.  You can derive great benefit from using your intuition in this way in all areas of your life. (p.26)

I stopped worrying about not having any good ideas, and practically the moment I relaxed, the answers I needed were there.  Now all I have to do is put them into practice!