Action Research, a medical research charity for serious disabling diseases, was the first to plead for donations to the fund to be made in addition to existing charitable gifts.
Anne Luther, its director-general, said that at least one supporter, who runs the marathon, had already switched allegiance. It was clear that some who had previously pledged their support to Action Research wanted to redirect their funds to be associated with a suitable memorial to the work which Diana had accomplished.
But Mrs Luther said: "I cannot believe that it would have been Diana's wish that the charities she espoused should benefit at the expense of other good causes: rather that we should all be prepared to go the extra mile."
Action Research was not a charity with which Diana had been associated, but its work "underpins much of what the Princess chose to face so compassionately". It had cancelled fundraising events last Saturday "out of our deepest respect".
But, while the fears might prove groundless, Mrs Luther said that if several hundred people who traditionally gave pounds 10 or pounds 20 did not do so, that would be a problem.
Barry Brooking, chief executive of the Parkinson's Disease Society, which Diana supported until her divorce, said Action Research had raised an important point and was brave to do so at such a sensitive time.
It was vital for charities like Parkinson's to maintain their income to be able to carry out their work. "There is a finite amount of money which is available to charities."
Details of the memorial fund were yet to be confirmed, although it seemed probable that the six charities of which Diana was patron would benefit, as well as perhaps the 100 or so more which she backed until her divorce. Mr Brooking said he could understand the fears of other charities. "This could mean there is less in the pot . But knowing Diana, she wouldn't want an imbalance."
Derek Bodell, of the National Aids Trust, one of the six charities which the Princess continued to support, said it believed that the distribution of the fund would have to reflect the totality of her interests.
"It doesn't serve anyone's interests if so much money goes in one direction that other good causes and charitable activities, not linked with Princess Diana, suffer."
Tony Manwaring, from NCH Action for Children, said: "For now, it's important that the public continue to give. The resounding popular response to Diana's charitable works is clearly a restatement of the values of helping charities."
Lindsay Bose, of the National Council of Voluntary Organisations, said"We would encourage people to continue in their normal course of giving in addition to this fund."