I almost always have a black cardigan as a go to cover up - bought one with gold buttons from Dotty Ps yesterday as cold and then a tote bag for summer. But I just recalled that generally I always used to buy summer dresses and then raffia/rattan/straw bags for summer, preferably with zips, sometimes vintage etc.
www.dorothyperkins.com/en/dpuk/product/khaki-gold-button-cardigan-8959749
uk.accessorize.com/view/product/uk_catalog/acc_1.7/6899980300