Website Down Detector, which monitors computer problems at large companies, said more than 1,000 people had complained about Lloyds by 11 a.m.
About 65% had problems with online banking and 35% with the app.
About 1,100 had reported problems with Halifax and 153 with the Bank of Scotland.
All three are part of the larger Lloyds Banking Group.
The issues started to be reported around 10:10 am.
Customers on Twitter said they were unable to access their accounts or transfer money.
A spokesperson for Lloyds Banking Group said, “We know that some of our customers are having intermittent problems logging into their banking services through our app and online. We are sorry and are working to get this back to normal soon. “
Two weeks ago, Lloyds Banking Group said it paid £ 13.6million to around 350,000 customers after a regulatory investigation into how he renewed home insurance policies.
Lloyds, along with Halifax and Bank of Scotland, told 2.7 million customers between 2009 and 2017 that their renewal price was competitive.
But the banks did not verify that it was fair, according to the supervisory body of the Financial Conduct Authority (FCA).
The FCA said this meant “serious harm to consumers” as most customers were charged more upon renewal.
During the same period, banks sent letters to about 500,000 home insurance customers telling them they would receive a renewal discount.