The American investment giant said the decision, which will lead to the loss of 260 jobs, was part of a strategy of focusing on its core asset management business.
Barry Bateman, chairman of FBS (UK), said: "As the UK financial services market changes rapidly and in view of the unique dynamics of the brokerage arena, we feel there are more opportunities in the investment management business."
But industry observers said it was obvious that Fidelity was ridding itself of an operation that had become a costly embarrassment.
Fidelity, which manages $600bn (pounds 360bn) world-wide, has poured tens of millions of pounds into retail stockbroking since it opened FBS in 1988. It currently enjoys a 15 per cent share of the market for retail stockbroking services.
The stockbroker ran into trouble in late 1996 when it gave incorrect statements to more than 500 customers about the value of their investments.
In May last year, it was fined pounds 220,000 by the Securities and Futures Authority, which regulates stockbrokers.
Fidelity blamed system errors but was forced to close to new business for six months. The incident damaged Fidelity's attempt to grow its business by offering a special kind of PEP. The self-select PEP allowed customers to deal in stocks and place orders with stockbrokers, within the tax-shelter of a PEP.
But last night Fidelity insisted the problems did not influence its decision to close the brokerage unit.
The company assured investors that they would not lose money as a result of the move. The closure, which will be complete at the end of February, is confined to FBS and does not affect Fidelity Investments, the fund management business with 500,000 customers.
- Andrew Verity