* NATO reputation could be damaged, MPs say
* Report urges Britain to give up anti-narcotics mission
By Adrian Croft
LONDON, Aug 2 (Reuters) - Other NATO allies should contribute more to fighting the Taliban in Afghanistan or risk damaging the alliance's reputation, British legislators warned on Sunday.
"The failure of some NATO allies to ensure that the burden of international effort in Afghanistan is shared equitably has placed an unacceptable strain on a handful of countries," parliament's Foreign Affairs Committee said in a report.
"There is a real possibility that without a more equitable distribution of responsibility and risk, NATO's effort will be further inhibited and its reputation as a military alliance, capable of undertaking out-of-area operations, seriously damaged," it added.
The report was issued after Britain suffered the loss of 22 soldiers killed in July, the deadliest month of the war during which Britain and the United States carried out major operations against Taliban insurgents in the southern province of Helmand.
Britain has more than 9,000 troops in Afghanistan, the largest foreign contingent after the United States, which had 41 of its soldiers killed in July.
The legislators did not specify which NATO allies they thought should contribute more, but Germany and other European countries have been under pressure from the United States to send more troops to Afghanistan.
Many have been reluctant, citing public opposition to greater involvement in the country.
The legislators also said Britain should give up the lead role in combating drug-trafficking in Afghanistan and focus on improving security.
Editing by Michael Roddy