Having searched online, I finally found a picture of the kind of cap I was looking for.
It is at the Met,. Museum, and they kindly put a couple of measurements. http://www.mfa.org/collections/object/woman-s-white-linen-cap-49971 I cut it out in paper and seeltaped it together, and gave me exactly the look I was after, so I went ahead and cut it in linen. I added a bit to the cap bit at the back of the head, because I have a big head - it can always be made smaller - and am going to baste it together any minute now. If it works, I will hire it to the customer, as I need a cap for someone else, and it will save me making two. The hired one is only needed for a limited time. Still wish I could find the Victorian one though!
I found lots of cap help here http://www.larsdatter.com/18c/womens-caps.html
I also, finally, cut out the shift pattern from "Costume Closeup" - it is a really useful pattern, and works really well. And cut two lengths of calico for a petticoat - phew, I'm exhausted after all that hard work! So I shall go and get changed into the green matka skirt I made recently, and go out for a meal with my DH and then to the theatre to see "School for Scandal".