Weaker property and utility stocks weigh on Britain's FTSE

* Utility, property stocks hit by rise in bond yields

* FTSE flat but still up around 6 pct since start of 2015

* Unilever (NYSE: UL - news) boosted by Barclays (LSE: BARC.L - news) upgrade

By Sudip Kar-Gupta

LONDON, June 3 (Reuters) - Britain's top equity index made little progress on Wednesday as a rise in bond yields hit utility and property shares, whose typically high debt levels make them particularly vulnerable to credit market jitters.

The blue-chip FTSE 100 index was flat at 6,931.05 points in early session trading, leaving the FTSE some 3 percent below a record high of 7,122.74 points reached in late April.

Property and utility stocks dominated the FTSE's loserboard. British Land (LSE: BLND.L - news) fell 1.7 percent, real estate rival Land Securities retreated 1.1 percent while utility National Grid declined 1.5 percent.

Traders said those sectors were being hit by a pick-up in British government bond yields, which rose along with German bond yields following a surprise increase in European inflation data. Lingering uncertainty over Greece's debt problems were also impacting the credit market.

"The market is showing some signs of nerves at the moment. In the long term, there's a lot of value in the FTSE, but it's looking a bit overbought at the moment," said Kyri Kangellaris, director at Horizon Stockbroking.

On the positive side, consumer goods group Unilever rose 1.4 percent after Barclays upgraded its rating on the stock to "overweight" from "equal weight", while plumbing supplies group Wolseley (LSE: WOS.L - news) rose 0.9 percent after posting higher profits.

The FTSE 100 remains up by around 6 percent since the start of 2015. (Reporting by Sudip Kar-Gupta; Editing by Dominic Evans)