Additional hardy white flowering shrub plants are:-
Azalea indica ‘Alba’
Rosa ‘Iceberg’
Natal plum (Carissa macrocarpa)
Clerodendrum incisum
White Poinsettia (Euphorbia pulcherrima ‘Alba’)
Orange Jessamine (Murraya paniculata)
Bangkok Rose (Mussaenda cultivars)
White Plumbago (Plumbago auriculata ‘Alba’)
False Gardenia (Tabernaemontana species)

More trees with white flowers include:-
White Christmas Jacaranda (Jacaranda ‘White Christmas’)
Bull Bay Evergreen Magnolia (Magnolia grandiflora)
Weeping paperbark (Melaleuca leucadendra)
Native Daphne (Phaleria clerodendron)

More white climbers worth trying:-
Bougainvillea – white forms
Frangipani vine (Chonemorpha fragrans)
Bleeding heart (Clerodendrum thomsoniae)
Madagascan Jasmine (Stephanotis floribunda)

With compliments from PLANT ID
www.plant.id.au