UPDATE 1-Sterling falls vs euro, steady vs dollar; support measures in focus

* Graphic: World FX rates in 2020 http://tmsnrt.rs/2egbfVh

* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Adds construction PMI and chart)

By Olga Cotaga

LONDON, July 6 (Reuters) - The pound fell against the euro and held steady against the U.S. dollar, as traders looked ahead to this month's Brexit negotiations and more government support measures expected later this week.

Traders expect more clarity by the end of July on whether Britain will agree a trade deal with the European Union. Britain left the EU in January, but it has full access to the bloc during a transition that runs until the end of December.

Britain and the EU need to make progress on access to EU financial markets. The coronavirus crisis will make it even harder to cope with disruption if there is no agreement, banking lobby AFME said on Monday.

The pound was unmoved by a business survey that showed British construction companies returned to growth in June for the first time since the coronavirus lockdown began, albeit from low levels.

Sterling was last down 0.4% against the euro at 90.43 pence and flat at $1.2485 against the dollar.

The pound remains 6% weaker so far this year, but it has recovered from the lows in mid-March, when it sank to $1.14, its lowest since 1985.

"Euro/sterling is consolidating above 0.90 and should remain range-bound into Wednesday, when Chancellor Rishi Sunak announces a fresh range of UK support measures in parliament," ING analysts said in a note to client. "A break under 0.90 in EUR/GBP would be a surprise," they said.

British finance minister Rishi Sunak is considering plans to hand out vouchers of 500 pounds ($624) for adults and 250 pounds for children, to spend in sectors of the economy hit hardest by the coronavirus crisis, the Guardian said on Sunday.

(Reporting by Olga Cotaga; editing by Barbara Lewis, Larry King)