The bank is the largest in Japan, where it faces more than 80 percent of all cyber attacks, but also provides corporate banking services in the UK.
Meeting at the Financial Times' Political Risk summit on Wednesday, the Bank of Tokyo-Mitsubishi and Lloyds Commercial Banking discussed the "new wave" of cyber-security threats.
They were joined by Jamie Saunders, director for the National Cyber Crime Unit at the National Crime Agency, and James Snook, deputy director at the business, crime and skills office for cyber security at the Cabinet Office.
The NCA's Jamie Saunders said it's "very easy to share information with government" and that if "any company thinks there's been criminality they can tell us about it".
But the Bank of Tokyo-Mitsubishi's Yuki Kataoka said: "We have been reporting our attacks but we don't seem to be big enough to be helped."
Lloyds' head of data and cyber security in data services, Giles Taylor, suggested there is a long way to go for information sharing between the private sector and government bodies, although it is now "starting to take off".
"I think at the moment, maybe we're not getting all the information we'd like back from government," Taylor said. "But we are confident there are some measures underway and some progress to make that happen."
The Cabinet Office's James Snook retorted that the government has heard from industry its approach to cyber security risk is far too complex at present - "you have the information sharing platform, you have any number of intelligence agencies and departments doing different things, which can make it difficult for industry to know where to go."
But he mentioned chancellor George Osborne's announcement late last year that there will be the establishment of a national cyber centre, with the intention of unifying government organisations that deal with cyber risk.
Lloyds' Giles Taylor said that one of the biggest challenges in information sharing is that a lot of front line businesses "don't really understand the risk - I don't think many people do, including myself. Sometimes I'll wake up in the morning, see an attack, and hadn't realised that was possible.
"Because this is such a fast-evolving space, it's very difficult for somebody to have that big picture," Taylor said. "It's very challenging when you start to put together the metrics, because there's this reluctance for people to admit they've been hit.
"So if you have a customer who's been impacted you may not know."
Taylor said that until businesses begin to get a handle on awareness and detection, it will become "very difficult" to quantify and put into a risk or big data model.
"It's almost a case of being able to detect that you've had a breach. One of the big challenges and differences with cyber over a more traditional event like flooding is if you've been flooded you know," he said.
"Sometimes if you've been attacked from a cyber perspective you may not actually realise that you've been attacked - and the first sign that you have been attacked may be someone else telling you."
"So because of that it's very difficult to quantify. It could be the data elements that are lost, it could be the financial transactions that will be part of that attack. The first thing is getting that detection capability and quantify things much better, and hopefully limit the ability of that attack."