Autumn is a really good time for transplanting work because the soil has sufficient moisture thanks to regular rain showers. The ground is still warm from the summer and autumn and so the plants still have enough time to get used to their new position and form new roots.
New plants can also be planted in autumn with a clear conscience. This is the last chance before the winter to bring a bit of colour into the garden. For roses, for example, autumn - before the first ground frost - is the ideal planting time.