Tory backbencher David Burrowes had written to Dominic Grieve, QC, earlier this month questioning the eight month terms for perverting the course of justice.
Mr Huhne's former status as a Cabinet minister and Ms Pryce's as a government economist should have been treated as aggravating factors, he insisted.
However, Mr Grieve has concluded that any challenge is unlikely to succeed. He said: "Having considered the sentences very carefully, I have decided not to refer them to the Court of Appeal as I do not think the court will increase them.
"The Court of Appeal has set out what 'unduly lenient' means in practice.
"The power to refer sentences under the regime is an exceptional jurisdiction, to be exercised only when the sentencing judge falls into gross error."
Mr Grieve wrote: "To be unduly lenient a sentence must be below the range of sentences which a judge, properly applying his or her mind to all relevant factors, could impose."
However, he said that did not seem to be the case with the terms that Lord Justice Sweeney had handed Huhne and Pryce for swapping speeding penalty points.
Meanwhile, Labour MP Andrew Gwynne has written to Prime Minister David Cameron urging him to push for action to strip Pryce of the title of Companion of the Order of the Bath.
He said it was "profoundly unacceptable" for her to maintain the honour which she was given for work as an economist for the UK Government.