The prospect of interest rate cuts and a flurry of bargain-hunting by stock market investors has helped the FTSE 100 shrug off the Brexit vote to hit a 10-month high.

In a strong start to the second half of 2016, the index of London-listed bluechip shares finished up 73.5 points, or 1.1%, on the day at 6,577.83. That built on solid gains clocked up over the previous three days and left the FTSE 100 up 7.2% over the week – the biggest weekly rally since late 2011, when hopes for a solution to the eurozone crisis had fired up the FTSE and other stock markets around the world.

This week’s rebound was a sharp contrast to just a week earlier when investors had woken up to the news Britain had voted to leave the EU. The referendum outcome last Friday caught traders off-guard after opinion polls had led them to bet on a remain vote. On the day the victory for the leave camp was confirmed, a record $2.08tn was wiped off the value of global shares.

But markets quickly stabilised in the days following the vote as investors saw the low prices of some stocks as a buying opportunity and as other stocks rose in the wake of the Brexit vote.

Shares in miners have been boosted by a rise in demand for precious metals, seen as a safer asset to hold in uncertain times. There were also big gains for companies that get a substantial amount of their sales from overseas thanks to a fall in the pound.

The drop in sterling, which has plumbed 31-year lows since the referendum, flatters the finances of those companies that report their profits in dollars. For example, while the banking sector has generally been battered by the Brexit vote, shares in the global bank HSBC which reports in US dollars are up 3.4% since the referendum.

The weaker pound has also boosted exporters because it makes their goods and services more competitive in overseas markets.

The latest fillip for stock markets came from the Bank of England governor’s strong hint on Thursday that interest rates could be cut within weeks and that policymakers were also ready to use other tools to shore up business and consumer confidence. Mark Carney said he believed “some monetary policy easing will likely be required over the summer”. In other words, official borrowing costs could be cut from their already record low of 0.5% as soon as a 14 July Bank policy meeting.

The prospect of official interest rates falling as low as zero increased appetite for shares, said Laith Khalaf, senior analyst at Hargreaves Lansdown. “The stock market likes falling interest rates though, and indeed the accompanying fall in the pound, so understandably the Footsie rose on the back of Mark Carney’s comments,” said Khalaf.

“In a world where you have to pay money to lend to the government, an investment in the stock market which pays you 3-4% a year looks attractive, even if it can be volatile.”

But there were doubts over whether stock markets could sustain their rally given the backdrop of political uncertainty in the UK and signs of a slowdown in the global economy that emerged long before the referendum.

“The big question is if the FTSE and [other stock markets] can hold on to the momentum they have accrued in the past few days, or whether the ongoing issues in the property and banking sectors, as well as the general sense of uncertainty that seems to be everywhere but the markets at the moment, will prove to be too much,” said Connor Campbell, analyst at spread-betting firm Spreadex.

While the internationally diverse FTSE 100 is at a peak for this year, the more domestically focused FTSE 250 of mid-sized companies has yet to return to its pre-referendum level. Seen as a better proxy for confidence in the UK economy, that index closed at 16,565.49 on Friday, up 1.2% on the day, but down on its 17,333.51 level the night the polls closed on 23 June.

Other European bourses were also struggling to regain their pre-referendum levels, with traders citing worries about the impact of Brexit on the rest of the EU, where some commentators fear a domino effect with other countries heading for the exit.

Italy’s main share index, weighed down by fears over some of its banking stocks, is down 9% since the referendum.