More than 360,000 people have registered for the launch of Paym, the mobile-to-mobile payments system launched on Tuesday morning.

Paym is backed by most of the major banks, including Lloyds, Barclays and HSBC, though not, initially, RBS/NatWest (it joins later this year), and will let customers send and receive payments directly to a current account using just a mobile phone number.

The Payments Council, the body coordinating the launch, expects 1bn Paym payments to be made by 2018 as bank customers use the service to make direct payments to people such as window cleaners and babysitters just by pressing a few buttons on their smartphones.

Customers will not need to remember or ask for sort codes or account numbers. They will be able to make a payment simply by selecting the person's number from the contacts list on their phone or by entering their mobile number. To receive money, people will have to register their mobile phone number to the service and select the account into which they want payments made.

Research by Consumer Intelligence, a polling company, found that 25% of bank customers said they expected to use Paym, rising to 39% among those aged 18 to 34. But nearly half said they definitely would not use the service, with most worried about security and the risk of money going missing.

A spokesman for the Payments Council said all the banks and building societies offering Paym have had to sign up to stringent security standards.