UPDATE 1-Sterling climbs after dollar sell-off, Hammond speech

* Sterling hits two-week high vs dollar

* U.S. inflation, Tillerson firing boost pound

* Graphic: World FX rates in 2018 http://tmsnrt.rs/2egbfVh

* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Writes through after Hammond speech, Tillerson ousting)

LONDON, March 13 (Reuters) - Sterling rose to a two-week high on Tuesday as the dollar sold off after data showed U.S. consumer price inflation in February cooled and President Donald Trump said he had fired U.S. Secretary of State Rex Tillerson.

As the dollar began its sell-off, British Finance Minister Philip Hammond gave his half-yearly economic update on the economy.

Hammond upgraded his growth forecasts a little and trimmed his budget deficit expectations, providing some extra wind behind sterling's bounce higher.

"Currency markets are generally supportive 1/8of tight fiscal policy 3/8," said Neil Jones, head of FX hedge fund sales at Mizuho. "The Trump firing of Tillerson is giving the pound a further boost on the back of a general dollar sell-off."

The pound rose 0.4 percent to a day high of $1.3970 , its best level since Feb. 27.

Against the euro, sterling gained 0.2 percent to 88.60 pence per euro.

Hammond said Britain's budget forecasters expect the economy to grow by 1.5 percent in 2018, up from a forecast of 1.4 percent in November. That would help the government lower its expected borrowing in the run-up to Brexit, he said.

"We did have confirmation that public finances are better than expected and that there will be scope for spending increases in future years. There were no immediate promises but he was clearly preparing the ground for a loosening of spending constraints in the next year or so," said Sarah Hewin, chief economist for Europe at Standard Chartered.

With Britain stuck in negotiations with the European Union to try to agree the terms of a transition deal to cover the period after it leaves the bloc, Brexit had been overshadowing other influences on the pound.

Renewed concerns about the state of Brexit talks after the EU rejected some British proposals for a trade deal last week had weighed on the pound in recent weeks, as had a recovery in the dollar. (Reporting by Tommy Wilkes Additional reporting by Sujata Rao Editing by Janet Lawrence)