Forget affordability. The toughest problem facing Treasury officials may be finding a way to make timely payments to some of the 5.3m households that are set to lose out from scrapping the 10p rate.

The rub is that if officials choose to keep Gordon Brown happy by using his cherished tax credits system, the lucky losers identified for compensation may be waiting for up to 18 months for their backdated cheque. This would coincide with the much heralded plans to raise the minimum wage, which will not come into force before October 2009.

I’m not convinced voters will be understanding about such a long wait.

Here is why it could take that long. The tax credits system is cumbersome and hard to manage. It works on an annual basis and is fiendishly difficult to adjust mid-year in any significant way. Monthly payments are set at the start of the financial year in April. A process of “reconciliation” then takes place in September, where overpayments and underpayments are calculated. (About 2m families are told at this point to give money back to the government because they have been overpaid. Great politics.)

A best case calendar for extending tax credits to those low-paid workers without children would look like this:

• November 2008: Alistair Darling announces the changes
• Jan/Feb/March 2009: People apply for tax credits for 2008 (effectively backdated payments) and 2009
• April 2009: Monthly payments begin that compensate for both the 2008 and 2009 financial year

A more realistic scenario was outlined to me by Ian Mulheirn of the Social Market Foundation, who wrote an excellent review of the options available to the chancellor.

“Amending the tax-credit system to assist these people would only take effect from April 2009 and any backdating in respect of 2008 would probably take another six months,” he told me. Basically, the backdated payments for 2008 would be calculated when it comes to “reconciling” the tax credit payments in September 2009.

This would effectively mean that even those lucky few chosen to receive compensation would be out of pocket until October 2009.

Is that a message that will win votes on the doorstep?

A far simpler and much quicker alternative, advocated by the Institute for Fiscal Studies, is to increase income tax allowances, a measure Gordon Brown has criticised in the past because it is more regressive than tax credits. Changing the income tax schedule was not mentioned by the Treasury in its letter outlining the 10p rate U-turn.

The question is: will the prime minister swallow his pride and admit that tax credits are not the best solution to his compensation puzzle?