(Recasts with closing prices) LONDON, Aug 6 (Reuters) - British two-year gilt yields jumped to their highest since April 2020 on Friday and 10-year yields also rose sharply, pushed higher by stronger-than-expected U.S. jobs data and a Bank of England promise of “modest” policy tightening. Two-year gilt yields rose as high as 0.162%, close to levels last seen during a period of market turmoil at the start of the COVID-19 pandemic which prompted the BoE to restart its bond purchase programme. On Thursday, the BoE set out the process by which it will start to reverse some of these purchases - although not before it has raised its main interest rate to 0.5% from the current 0.1%, which markets do not price in before 2023. The BoE said it expected some modest tightening of monetary policy to be needed over the next 2-3 years, and following which markets have brought forward their expectation for a first rate rise, to 0.25%, to May 2022 from August 2022. “We do think it’s more likely than not that some moderate tightening of policy ... will be necessary,” BoE Deputy Governor Ben Broadbent told businesses on Friday, adding that he would be paying particularly close attention to labour shortages. Since the BoE’s announcement, two-year gilt yields - which are sensitive to expected changes in the BoE’s Bank Rate - have risen 8 basis points, their biggest two-day rise since February. Stronger-than-expected U.S. non-farm payrolls data - coming in the wake of weak ADP private-sector payrolls numbers the day before - drove a rise in U.S. Treasury yields and also pushed up gilt yields, which usually closely track Treasuries. Ten-year gilt yields recorded their biggest daily gain since March, rising 9 basis points, and touched their highest since July 22 at 0.623%. “Today’s non-farm payrolls release, and recent news on the bipartisan U.S. infrastructure bill, add some weight to our view that the past week’s climb in U.S. Treasury yields and steepening of the yield curve have further to run,” said Oliver Allen, markets economist at Capital Economics. (Reporting by David Milliken and William Schomberg Editing by Mark Potter) Our Standards: The Thomson Reuters Trust Principles.