The sector bodies were responding to the Treasury consultation Gift Aid and Digital Donations, which closed on Friday.
The consultation sought views on subjects including what any future universal Gift Aid donor database might look like. It says that the government has no current plans to build or operate such a system, but it would consider how it could support its introduction if a suitable model could be developed.
The IoF says in its response that it sees the potential benefits of moving to such a system, but cautions that it would need significant investment and could carry risks.
It also raises concerns about requiring people to fill in a single declaration and submit it to a separate database rather than making the declaration at the point of donation.
Daniel Fluskey, head of policy and research at the IoF, said: "There are some positive proposals in the consultation, particularly around shortening the declaration, which we welcome. However, for these to be a success the complexity that surrounds them needs to be stripped away. Simplicity is the key: donors and charities want a simple system that works best for all."
One of the Treasury’s proposals includes shortening the Gift Aid declaration to 52 words instead of 111. Another is transferring liability for tax from the donor to the charity - under existing rules, the donor has to make a refund if it turns out he or she has not paid enough tax to cover the Gift Aid. The proposed new rule would make the charity liable.
Both CAF and the IoF urged the government not to adopt the "threatening" wording of the new shorter declaration as proposed in the consultation.
"The sentence ‘HMRC will check and may tell the charity if I have not paid enough tax’ would not be welcomed as it creates a negative and potentially very off-putting message to the donor, which would likely hinder any increased take-up," says the IoF’s response.
Rhodri Davies, head of policy and campaigns at CAF, told Third Sector it was in favour of any move to make Gift Aid simpler, which was the spirit behind the proposal to shorten the declaration.
But he raised concerns that the merits of the shorter declaration were not significant enough to outweigh the cost of shifting liabilities from the individual donor to charities.
"There is a fundamental concern about shifting the liability because it changes the risk profile of the whole system for charities and could have a damaging effect on the relationship between donors and charities," Davies said.
"If someone chooses to give to a cause they care about, it should be a case of the charity saying ‘thank you’; the first question should not be ‘can we have a breakdown of your tax affairs?’"
Talking about the new wording proposed for the declaration, he said: "It is hard to believe it will have a material impact on whether people choose to Gift-Aid their donations. It is a threatening sentence to include."
Davies said CAF’s response to the Treasury made it clear that a universal declaration linked to a donor database is the only option that would make a significant difference to the scheme.
"We’ve always pushed for a universal declaration linked to a donor database, which we feel has the most potential to make a big difference," he said.
It would benefit Gift Aid generally as well as specifically through online and mobile giving channels, he said.
"If the government really wants to make a significant impact in this area, that is what they need to take forward. But we recognise it is the least likely option to move forward quickly, as there are cost implications and questions about how it would be done."