* FTSE 100 closes down 0.1 pct at 6,813.49 points
* ECB cuts interest rates to record lows
* European stock markets rally as euro ticks lower
* But sterling rises, hindering FTSE
LONDON, June 5 (Reuters) - Britain's top equity index fell on Thursday, missing out on a broader rally among Europe's stock markets which were boosted by new European Central Bank (ECB) economic stimulus measures.
Traders said the UK's benchmark FTSE 100 index was hindered by the fact that the ECB's measures had led to the sterling currency rising against the euro, since a strong pound can impact the ability of British companies to export overseas.
The ECB cut interest rates to record lows on Thursday and unveiled new measures to strengthen the region's economy and fight off the risk of Japan-like deflation.
Although this caused European stock markets to rally, with Germany's DAX briefly hitting a record high of just over 10,000 points, the FTSE 100 underperformed.
The FTSE closed down by 0.1 percent, or 5.14 points, at 6,813.49 points - paling in comparison to gains of 1.1 percent on France's CAC and a 0.2 percent rise on the DAX.
"The FTSE is getting left behind. The DAX keeps breaking new record highs, but the FTSE keeps coming up short," said Central Markets trading analyst Joe Neighbour.
The FTSE hit a peak of 6,894.88 points last month, which marked its highest level since December 1999.
The index is up by around 1 percent since the start of 2014, but some traders said it needed to break out above the 7,000 point level - which would mark a record high for the FTSE - in order to start a stronger rally on the market.
"We have yet to test the psychological level of 7,000 in the FTSE. I feel that this alone could be a major turning point in the direction of the UK stocks," said Intertrader chief market strategist Steve Ruffley. (Additional reporting by Tricia Wright; Editing by Toby Chopra and Susan Thomas)