* Euro zone economic sentiment dips in June

* Copper prices still to fall to year-end on rising supply -UBS

* Coming up: Fed Chair Yellen speaks at ECB event at 1330 GMT

(Adds details, quotes; changes dateline from MELBOURNE)

By Eric Onstad

LONDON, June 29 (Reuters) - Copper retreated from the highest levels in nearly eight weeks on Wednesday as investors paused amid uncertainty about Britain's vote to exit the European Union and the outlook for mine supply.

Three-month copper on the London Metal Exchange had shed 0.3 percent to $4,804.50 a tonne by 1013 GMT, having earlier risen to the highest since May 5 at $4,831.50, following a 2.3 percent gain in the previous session.

"We have seen quite significant price rises this week and maybe yesterday it went a bit too far, so I'm not surprised the market is taking a breather today," said analyst Daniel Briesemann at Commerzbank in Frankfurt.

After touching a low of $4,588 on Friday after the UK Brexit vote, copper rallied by about 5 percent to touch Wednesday's peak as investors bought futures to cancel short positions and hoped for more global stimulus measures.

Highlighting the lack of clarity about the impact of Brexit, the Scottish first minister made a dash to Brussels to tell the EU that Scots were intent on staying in the bloc.

Sentiment was also dampened after data showed that Euro zone economic sentiment dipped in June.

There was division among analysts about whether the copper market would see more mine supply in coming months.

"Beyond the short-term gyrations, the bias for copper is for it to still ease from here through the rest of the year. Demand is positive but it's not spectacular and many signals point to a copper market that is well supplied," said analyst Daniel Morgan at UBS in Sydney.

While copper stocks on the Shanghai Futures Exchange have dropped by 60 percent since March, LME stocks surged by nearly 40 percent in early June, as traders relocated metal to cheaper storage and as price differentials favoured exports to global markets.

Briesemann, however, disagreed with forecasts that ample supply would knock the market in the second half of the year.

"I personally think that many market participants are too optimistic regarding supply and there is clearly scope for disappointment."

LME aluminium dipped 0.1 percent to $1,622 a tonne as producers sold to lock in firmer prices.

There was also concern that the world's biggest producer China, after signs of curbing aluminium output late last year, was gradually increasing output again, raising the risk of fresh tensions with global trading partners from any spike in exports.

(Additional reporting by Melanie Burton) ((eric.onstad@thomsonreuters.com; +44 20 7542 7093; Reuters Messaging: eric.onstad.thomsonreuters.com@reuters.net))