A statement from the company, a subsidiary of Dollar Financial UK, revealed the closures may be necessary following after new regulations on consumer lending were introduced.
As yet no workers at the Money Shop on High Street, Hucknall, had been told if they will be made redundant.
The will also close one of its three UK head offices, with its Bromley operation most likely to be shut.
The statement said: “Regrettably, it is possible that some 350 redundancies may be necessary as the company evolves its business to serve customers in a fair and sustainable way following the introduction of the new regulations on consumer lending, as well as removing duplication of facilities inherited through previous acquisitions.
“We fully acknowledge the impact these proposals may have on our people both personally and professionally and we will support affected employees through this process and into future employment.
“Dollar Financial is committed to ensuring that the business review is undertaken in a way that allows a comprehensive consultation and communication process with those likely to be affected.”