UK's FTSE pegged back by weak mining stocks and Greek worries

* Fall in copper prices weighs on mining stocks

* Citigroup (NYSE: C - news) downgrade impacts Admiral

* Sage lifted by Investec (LSE: INVP.L - news) upgrade

By Sudip Kar-Gupta

LONDON, June 25 (Reuters) - Britain's top equity index slipped on Thursday from three-week highs reached in the previous session as weaker mining stocks and persistent concerns over Greece's debt problems weighed on the market.

The benchmark FTSE 100 equity index was down by 0.4 percent at 6,816.57 points going into the close of the trading session.

Miners took most points off the index, with the FTSE 350 Mining Index falling 1.1 percent as copper prices lost ground.

The FTSE 100 is some 4 percent below a record high of 7,122.74 points reached in April. The worries about Greece's fate have knocked back European stock markets in the last month.

Without a cash-for-reform deal in the next 48 hours, the chances of Greece averting a default to the International Monetary Fund look slim.

Failure to repay 1.6 billion euros ($1.79 billion) owed to the IMF next week could trigger a bank run and capital controls, and the risk of Greece sliding out of the euro currency area.

"I don't think we'll see much major progress until the Greek situation becomes clearer," said Central Markets trading analyst Joe Neighbour.

Insurance company Admiral fell 1.9 percent after Citigroup downgraded the stock to "sell" from "neutral".

However, software company Sage rose 4 percent to recover from hefty losses in the previous session as Investec Securities raised its rating on the stock.

($1 = 0.8931 euros) (Additional reporting by Alistair Smout; Editing by Gareth Jones)