Home Secretary Theresa May has promised to look at perceived difficulties in cracking down on licence breaches at pubs and shops.
Congleton MP Fiona Bruce told Parliament that licensing officers in Cheshire had found procedures to take enforcement action "unwieldy and protracted, even when a sale to an under-age individual has occurred".
She asked: "Will the minister look into enforcement difficulties, such as problems identifying which salesperson to prosecute, the tactic of a swift change of a named licence holder making closure notices hard to apply and the omission of a power to require mandatory staff retraining?"
May said it's "important" to change not just legislation "but to ensure that enforcement takes place properly".
"I am sure we will be happy to look at the particular issues that she raises in relation to the difficulty of enforcement."
May said she expected the ban on below-cost alcohol sales to mean 7,000 fewer alcohol-related incidents and 1,000 fewer hospital admissions.
But Keith Vaz MP, who chairs the Home Affairs Committee that has looked at the issue, urged May to make the crackdown on cheap alcohol sales a "genuine exercise, but just a box-ticking exercise".
He flagged up the fact that the proposed below-cost ban would prohibit sales below 21p per unit and health campaigners want a 50p minimum.
Elsewhere, Hull MP Diana Johnson feared the proposed late night levy could become "an additional tax burden on local businesses" while the policing they receive still falls due to the 20% cut in police budgets.
May was also asked whether she agrees that licence enforcement is one area that should not be cut as police forces make cost savings.
She said: "It is not for us to tell chief constables how to allocate their resources, but they will look to ensure that they have the right mix of police officers and police staff to ensure that the licensing law is abided by and enforced."