Barclays shares were suspended after falling more than 10 per cent, while Royal Bank of Scotland fell more than 14 per cent, reports The BBC.
Easyjet’s fall came after the airline said revenues would fall more than expected, partly because of Brexit.
Overall, the FTSE 100 fell more than 1 per cent at 6,071,76 by mid-morning, but the fall was not as bad as some had feared.
Property shares were also badly hit on worries that the decision to leave the EU would hit the housing market. Taylor Wimpey and Barratt Developments both fell about 12 per cent.
The FTSE 100 had plunged more than 8% at one point on Friday before recovering some ground to close 3.2 per cent lower.
The FTSE 250 index, which mostly contains companies that are more UK-focused, was down 3.5 per cent on Monday after sliding 7 per cent on Friday.
The pound hit a 31-year low of $1.3221, sinking below the level it had fallen to on Friday, when it recorded its biggest one-day fall against the dollar.
The return on UK government bonds – known as the gilt yield – fell to its lowest level ever on Monday.
Investors are buying more UK government debt in search of safer investments.
The yield from a 10-year gilt dropped below 1% for the first time – hitting 0.993 per cent in morning trading.
In a statement issued before the UK stock market opened, Chancellor George Osborne said the UK was ready to face the future “from a position of strength”.
He also indicated there would be no immediate emergency Budget. Mr Osborne said there would still need to be an “adjustment” in the UK economy, but added it was “perfectly sensible to wait for a new prime minister” before taking any such action.
“Markets seem a little calmer this morning, which we can at least partially attribute to George Osborne’s statement,” said Joe Rundle, head of trading at ETX Capital.
“After going to ground since the vote, the chancellor’s appearance indicates some much-needed continuity at the heart of government.
“Despite the prime minister’s resignation and a swathe of Labour shadow cabinet departures, [Mr] Osborne doesn’t appear to be going anywhere.”
