No. You are entitled to be paid an average basic hourly rate of at least the National Minimum Wage for all the hours you spend working. This includes any time you are required by your employer to spend waiting "at or near the workplace" (other than at home), to see if work is available. It doesn't matter whether this time is described as 'on-call', 'standby' or 'downtime'. If you are required to be available for work at or near the workplace, you are entitled to be paid.
The National Minimum Wage is calculated using a period of time called a ‘pay reference period’. This will be a week if you are paid weekly, a month if you are paid monthly and a day if you are paid daily. In order for your employer to comply with National Minimum Wage law, your average basic hourly rate for all the hours you work during the pay reference period (including any time when your employer requires you to wait at or near the workplace to see whether work will become available) must be at least the National Minimum Wage.
You can check the position using the workSMART National Minimum Wage calculator.
If you have a zero hours contract, your contract terms probably allow your employer to tell you at short notice when you are needed and to send you away when you are not needed, but as a minimum, you must be paid for the time you are required to spend waiting "at or near the workplace".
Have a look at your contract terms and show them to your union rep if you are unsure.
The TUC campaigns for much stronger protection of zero hours contract workers, including compensation when zero hours shifts are cancelled at short notice. The best way of improving your position is by joining a trade union and encouraging your workmates to do the same, so that better terms can be negotiated by the union through collective bargaining. Browse our Union Finder tool for more information.