IAG and Royal Mail fall as UK's FTSE hits five-month low

* FTSE 100 at lowest level since late January

* Greek debt woes and U.S. rate hike prospect hurt sentiment

* Fall in Air France (Paris: FR0000031122 - news) weighs on IAG

* Royal Mail (LSE: RMG.L - news) hit by prospect of UK rules review

* APR Energy (Other OTC: APRYF - news) down nearly 30 pct after profit warning

By Sudip Kar-Gupta

LONDON, June 16 (Reuters) - Britain's main share index slid to a five-month low on Tuesday, with investors unnerved by a deadlock in Greek debt talks and the prospect of a rate increase by the United States in September.

The FTSE 100 equity index fell 0.4 percent to 6,683.58 points, its lowest level since late January.

International Consolidated Airlines Group (IAG) was among the worst-performing FTSE 100 shares, falling 2.8 percent after a slump at rival Air France KLM weighed on European airline stocks.

Air France's shares fell 4 percent after the company said it was dropping some routes to cut costs.

Postal services provider Royal Mail retreated 1.9 percent after a British watchdog agency said it would review the regulation of the former state-owned firm after the withdrawal of its only competitor.

Among small caps, APR Energy slumped nearly 30 percent after warning that its 2015 results would be significantly below market expectations.

The FTSE is some 6 percent below a record high of 7,122.74 points reached in late April, as concerns over Greek debt push European stocks down from their 2015 peaks.

Greece and its creditors have hardened their stances this week after the collapse of talks over the weekend aimed at preventing a default and possible euro exit.

"Crisis fatigue has gone from acute to chronic at this point and even the much-maligned and underestimated contagion factor is beginning to rear its head as peripheral bond yields head higher in concert with that of Greece," said London Capital (LSE: LCG.L - news) Group head analyst Brenda Kelly.

Also weighing on equities was the prospect of the U.S. Federal Reserve signalling that its first rate increase in nearly a decade will come in September, traders said.

Stocks rallied in recent years partly because record-low interest rates made cash and bonds less attractive. Higher U.S. rates would boost returns on U.S. Treasuries and reduce the appeal of equities. (Editing by Larry King)