Over 5 million - mainly customers of the Nationwide Building Society - will not be able to use the system fully until 2015.
The technology allows people to pay or receive money using a phone number, but without giving out their bank details.
All account holders need to do is to share the number of their mobile phone.
However around 30m customers of banks including Barclays, Bank of Scotland, Halifax, HSBC, Lloyds, Santander or TSB will now be able to use the service, as soon as they have registered their mobile number with their bank.
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Register your mobile number with your bankUse payments app to select friend's mobile numberConfirm recipient, then press 'send'You can send up to £250 a dayYou still receive money, even if your phone is switched offNo need to give out sort code and account numberThey will be able to send up to £250 a day on their mobile phones through Paym, although some banks offer a higher limit.Computer problems Customers of RBS, NatWest, Ulster Bank, First Direct, Clydesdale and Yorkshire banks will be able to join the scheme later this year.
The RBS group has over 13m current account holders, and First Direct has 1.2m.
However those with current accounts at the Nationwide will not be able to make payments until next year.
Other banks, including Metro Bank and some of the smaller building societies, have not set a timetable for joining the scheme.
RBS, whose customers have faced a series of computer problems over the last year, said it was giving priority to improving its IT systems.
"We are prioritising the volume of system changes we are making to ensure we can deliver the best service to our customers. ," said an RBS and NatWest spokesperson.
The reluctance of some banks to be ready for the scheme's launch is not the only problem.
A survey from the market research company Consumer Intelligence suggests only a quarter of customers will be using it.
'Like a balloon'The survey, conducted earlier this month, claims that 47% of account holders will not be using Paym at all.
Their biggest worry is security.
"It's clear that the banking industry has a job to do educate many of them that mobile payments are a safe and consumer-friendly development," said David Black of Consumer Intelligence.
Others have warned consumers to watch transactions on their accounts very carefully.
"They will need to be vigilant and monitor their accounts to make sure that there is no suspicious activity, as with every advance in banking technology comes a new fraud risk," said Gabriel Hopkins of the from the data consultancy FICO.
"Fraud is like a balloon - if you squeeze it in one place, it bulges somewhere else - so banks need to stay alert and have the highest level of mobile fraud protection for customers," he said.
But the Payments Council, which is running the scheme, insists the technology is perfectly secure.
Customers still have to access their accounts through a banking app, which is password-protected.
Paym is a "safe and easy option", said Adrian Kamellard, the chief executive of the Payments Council.
Account holders can find out more from their bank's website, or by visiting the Paym website.
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