Mothercare have some but not sure if they are all lined.
I got one for my dd when she was about 6 months (i.e. too young for one) from Pumpkin Patch years ago. It was a couple of years before she could wear it but is fab - red with big pink spots. They ahd matching boots and umbrellas but I drew the line at those
If I could persuade her to part with it, I'd offer it to you but no doubt she'll still want to waer it this summer although it is too small