Sterling jumps on reports of progress in Brexit talks

* Pound rises back above $1.30, hits one-week high

* Reports that Brexit talks improving help fuel rally

* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh

* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Adds details, updates prices)

By Tommy Wilkes

LONDON, April 30 (Reuters) - Sterling rose above $1.30, hitting a two-week high, on Tuesday after media reports that the tone of Brexit talks between the British government and the main opposition party had improved.

Prime Minister Theresa May is seeking a consensus with Labour to get a Brexit deal approved and wants talks to reach a conclusion by the middle of next week, several British journalists reported on Tuesday.

The pound rose to as high as $1.3049, with broad dollar weakness and end-of month portfolio changes by asset managers cited as possible reasons for the move alongside the Brexit-related optimism.

The British currency had fallen to a two-and-a-half-month low last week as the dollar surged and worries mounted about a deadlock in talks over the terms of Britain's exit from the European Union.

But the Times newspaper reported on Tuesday that May's government has made substantive moves in Brexit talks with Labour, citing unidentified Labour sources.

The EU hopes Britain's two biggest political parties will reach agreement on Brexit this week, possibly including membership in a customs union, the EU's chief Brexit negotiator said.

May agreed a withdrawal deal with the EU last year, but it was rejected three times by a deeply divided British parliament. That delayed the exit date, a postponement that has weighed on the pound as investors fret about prolonged political uncertainty.

The pound was on track for its biggest daily gain in over a month versus the dollar, rising 0.8 percent to $1.3047 and 0.6 percent to 85.91 pence against the euro.

Sterling traded as low as $1.2851 last week as the dollar surged towards two-year highs, measured against a basket of currencies.

"May is still under pressure to pass her deal; however, we don’t see a breakthrough anytime soon," Nordea analysts said in a note.

"Instead, we expect May to be ousted over the summer, leading to another extension beyond October 31. This postpones a BoE (Bank of England) hike and should weigh on GBP."

The Bank of England announces its interest rate decision on Thursday. Traders will search Governor Mark Carney's comments for signals that the central bank is ready to raise rates to tame inflationary pressures - although few analysts expect an increase before Britain's departure from the EU is clearer.

(Reporting by Tommy Wilkes and Tom Finn; Editing by Alison Williams and Ed Osmond)