The move, outlined in a letter from the chairman, Sir Andrew Hugh Smith, to exchange members, is likely to raise eyebrows in the City following the Taurus debacle, which cost firms more than pounds 300m.
Development of a new system was handed to the Bank of England after the fiasco.
The exchange wants to act as a manager of Crest during the transition from the Talisman share- settlement system.
The exchange also proposes to take about a 30 per cent stake in Crest in order to prevent fragmentation of the ownership of the system. Too many owners could lead to a lack of direction, it says.
This contrasts with the Bank's proposals that a manager for Crest should only be appointed by the new owners of the system. The Bank envisages ownership to be decided by the end of May.
The Stock Exchange says that the initial management of the system needs to be decided sooner rather than later in order to ensure a smooth transition from the old system.
The Bank has also suggested that no individual owner should have more than a 10 per cent stake, and no sector more than 30 per cent.
Sir Andrew wrote: 'The exchange believes it should participate in the ownership structure provided this can be achieved on a satisfactory basis. To do so on the basis of a significant minority interest would best contribute to the effectiveness of the arrangements.'
The exchange's proposals stop short, however, of taking on a management role beyond the transition stage.
Sir Andrew reiterated the exchange's support for the introduction of 10-day rolling settlement, which will replace the existing account system on 18 July.
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