LONDON, July 6 (Reuters) - British government bond yields hit fresh record lows on Wednesday as investors continued to buy sovereign debt as a shelter from the fallout to the country's decision to leave the European Union.

The yield on 10-year gilts fell to as low as 0.731 percent, almost half its level on June 23, the day when Britons were voting in the referendum, which many investors had expected to result in a decision to stay in the EU.

Yields on British 20- and 30-year government bonds also sank to fresh record lows on Wednesday.

Gilt futures rose more than 50 ticks to new contract highs of 130.47.

Fear of further instability in the EU and of weak global economic growth ahead sent stock markets sharply lower on Wednesday and Britain's pound sank below $1.30 for the first time in more than three decades.

(Writing by William Schomberg; Editing by Ana Nicolaci da Costa and Kevin Liffey)