Under previous hosepipe and sprinkler bans the use of watering cans, buckets and other water carrying devices has been perfectly acceptable for watering the garden, or for instance washing your car. During a ban you should always check with your local water company to see the specific rules they have in place of course.
It has also been generally accepted by the water companies in the past that a short piece of hose connected to a tap can be used to fill the watering can/bucket. Hence you’re actually using a hosepipe during a hosepipe ban!
The whole point of banning hosepipes and sprinklers is that they will tend to be left on for long periods of time and use up large amounts of water. Forcing you to use a watering can or bucket reduces the risk of using too much water.