BBC contacted over tax arrangements
The Chief Secretary to the Treasury has written to the new BBC director general over the tax arrangements of thousands of members of staff at the corporation.
A Public Accounts Committee report says too many make their own arrangements to pay tax and national insurance, which could allow them to contribute less.
The report found that in total some 2,400 civil servants were subject to such "off payroll" arrangements.
The BBC said it was carrying out a detailed review of tax arrangements.
The Public Accounts Committee (PAC) began its inquiries into "off payroll" contracts across the public sector after a BBC Newsnight investigation revealed earlier this year that the former head of the Student Loans Company was being paid via a company.
The arrangement - agreed by the tax authorities - potentially saved Ed Lester tens of thousands of pounds in tax.
It triggered a Treasury investigation across the government, which revealed that for more than 2,400 civil servants, tax was not being deducted when their wages were paid through PAYE.
The report also said it was shocked to find the BBC had 25,000 such off payroll contracts - 13,000 for people who were on air.
Mr Alexander said: "I've written to the new director general of the BBC, drawing his attention to the review we undertook, and suggesting that this might be something the BBC wants to look at.
"Clearly the public accounts committee agrees with that."
Committee chairwoman Margaret Hodge said: "It was... shocking to find out that no fewer than 2,400 central government appointees were benefiting from off payroll arrangements.
"Furthermore, the Treasury Review only covered civil servants. Tax avoidance in the public sector goes much wider."
The Labour MP said avoiding tax and national insurance when paying public sector staff was "almost always staggeringly inappropriate".
She urged the public sector to "show leadership in the fight against tax avoidance" and should avoid the practice of using off-payroll arrangements for staff.
Jonathan Isaby, political director of the Taxpayers' Alliance, which campaigns for lower taxes, said many people would be "astonished" by the findings.
"People are paying huge amounts of tax as it is for this country and they will feel even more angry if they think that those in public bodies, in the government, in local councils, and indeed their favourite TV presenters, are not paying their fair share as well," he said.
John Whiting, director of tax policy at the Chartered Institute of Taxation, said some workers make their own tax arrangements for legitimate reasons.
"What this report is targeting are people who are in what is often termed as 'disguised employment' - they're really an employee but they are putting the aura around them of 'No, I'm operating for a company'."
This, he said, was the charge being made against some BBC staff and some public sector workers.
Mr Whiting said the authorities did have a "notorious" anti-avoidance provision to deal with this, named IR35, which has been operating since 2000, however the MPs' report pointed out that this provision was "not that easy to apply" and it was not being applied in as many situations as it could be.
The committee said it still lacked full information about the number of people employed by the National Health Service or in local government who were paid through private companies.
Members acknowledged that ultimately, whether or not staff with off payroll contracts were paying the right amount of tax was dependent on HM Revenue and Customs properly enforcing the rules.
'Complying with legislation'
But they also expressed concern that in recent years, HMRC had reduced its enforcement of legislation designed to eliminate tax avoidance through the use of intermediaries.
The BBC said that the actual number of people who were not paying tax at source was far smaller than the figures suggested.
In a statement, the broadcaster said: "In many cases an individual - such as an occasional contributor to programmes - could be issued with a contract each time he or she is booked to appear.
"We note the conclusions of the PAC report and will respond to the points raised as part of our detailed review of tax arrangements."
David Smith, the BBC's head of employment tax, said the corporation was "complying with the legislation that is there".
Mr Smith said: "It's not necessarily staff positions we are using the service company route for.
"These are people who are freelance by their very nature, or certainly that's the way their services want to be provided to the BBC and the use of the service company is therefore there to protect the BBC from any unexpected exposure should HMRC disagree with that position."