* Graphic: World FX rates in 2018 http://tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Writes through after PMI release)
LONDON, July 3 (Reuters) - The pound rose on Tuesday as a rebound in risk appetite supported sterling and after a survey showed Britain's construction industry enjoying its fastest growth in June in seven months.
Chinese central bank comments on keeping the yuan stable, as well as broader moves higher for assets such as stocks, boosted currencies across the board including sterling.
The British currency rose 0.4 percent versus the dollar to as high as $1.3196, away from 2018 lows hit last week of $1.3050. Sterling made most of those gains before the construction survey numbers were released.
The Construction Purchasing Managers' Index (PMI) picked up to 53.1 from May's 52.5, better than forecast. It was the third month in a row that the sector grew after contracting in March.
Versus the euro sterling strengthened 0.2 percent to 88.44 pence.
Sterling has struggled in recent weeks as worries about whether Britain can secure itself a deal with the European Union before it leaves the bloc next March weigh on the currency.
On Monday it fell despite relatively robust manufacturing survey data as investors worried about a looming a Brexit cabinet meeting later this week.
"We're still wary that euro/sterling is on the verge of an upside break-out given its exit from a period of very low volatility. PM May looks set to face down the Brexiteers later this week, but may be no closer to a Brexit deal," ING analysts said in a note.
Adam Cole, currency strategist at RBC, said the construction PMI was the least interesting of the three PMI releases this week but the numbers will help build up the survey-based estimate of second quarter GDP, which will help determine if the Bank of England raises interest rates in August or waits. (Reporting by Tommy Wilkes; editing by David Stamp and Kirsten Donovan)