Fraudsters posing as TalkTalk workers have switched their caller ID - the incoming number which appears on mobile phone screens - to that of The Flower Shop in Caversham, Reading.
The shop said "confused" callers asking for the telecoms firm had started contacting them on Friday.
The case is being assessed by the National Fraud Intelligence Bureau.
A TalkTalk spokesman said: "We can confirm that this incident is not related to TalkTalk."
Shop manager Denika Potter said some of those ringing the business had been abusive after the fraudsters had tried to dupe them into providing their bank details.
She said many people recognised they were being targeted by scammers, but mistakenly thought the call had originated from the florist.
"Most customers are nice, accept it and apologise," said Ms Potter.
"Some are very annoyed, which you obviously may be if you are getting lots of missed calls from a number."
She said the calls were "disturbing" her staff's daily work and added:  "We are a small business and we're having to stop to answer the phone all the time."
An Action Fraud spokesman said it could take up to 28 days to determine whether there were "sufficient lines of enquiry for an investigation based in the UK".

Members of the technicians' union Bectu and the National Union of Journalists (NUJ) voted in favour of industrial action in protest at a 2% pay award.
Unions have been pressing for a bigger wage increase in view of the TV company's profits.
ITV said it was "confident" that viewers would be unaffected.
Good Morning Britain and the filming of soap operas are among the programmes could be hit.
ITV's pre-tax profits - including exceptional items - rose 39% to Â£605m for 2014.
Bectu general secretary Gerry Morrissey said staff were "very unhappy" with the pay offer.
"There is a huge disparity between the pay offered to staff and the bonus package to executives as well as shareholder dividends.
"Our members are helping to make the profits but are not sharing in them."
An ITV spokesman said: "We are fully prepared to maintain an open dialogue with union representatives following the ballot result, which saw 226 union members voting to strike out of a UK workforce of 3,000 employees.
"We have contingency plans in place to ensure that our programmes will continue to be broadcast and are confident that viewers will be unaffected by the proposed industrial action."
A family-run florist says it is being besieged with up to 120 calls a day in a phone cloning scam.
[NEXT_CONCEPT]
ITV staff are staging a 24-hour strike and planning a protest outside the broadcaster's annual meeting, in a dispute over pay.