Results from Britain's part-nationalised banks and oil giants BP and Royal Dutch Shell will guarantee a significant week for investors.

New Barclays boss Antony Jenkins will deliver his first set of figures on Thursday as the banking sector falls under the spotlight again in the third-quarter results season.

Mr Jenkins, formerly head of retail, took up the position of chief executive in August as Barclays reputation was in tatters from the fallout of the Libor rate-rigging affair.

Barclays is expected to unveil adjusted pre-tax profits for the three months to September 30 of £1.7 billion, up 27% on the same quarter in the previous year.

But this will not include an additional £700 million hit for covering the cost of mis-sold payment protection insurance claims nor a £1.1bn own credit charge.

The PPI mis-selling affair is just one of a series of reputation-scarring scandals to have hit Barclays along with rigging Libor.

Lloyds Banking Group is facing an additional charge for mis-sold PPI claims of up to £1.5bn in its third-quarter update on Thursday, brokers Credit Suisse have warned.

The forecast was made in light of the extra £700m set aside by Barclays and takes into account the size of Lloyds' loan book.

The total bill for the part-nationalised lender would as a result soar to nearly £6bn and is bound to leave taxpayers wondering when they will get their money back.

Fellow bailed-out lender Royal Bank of Scotland has been making similarly strong progress – when one-off factors such as PPI and its costly recent IT glitch are discounted.

The 80% state-backed lender is forecast by Credit Suisse to report pre-tax losses of £1.8bn, although this will be largely driven by an accounting effect on the value of its own credit.

Next is unlikely to spook investors with its trading update on Hallowe'en as the high street giant reveals another rise in sales. The fashion and homewares chain, which has around 540 stores, is forecast by brokers at Panmure Gordon to report a 1% rise in sales at its stores and a 14% increase in sales on its website Next Directory in the three months to October.

Oil giant BP will face questions tomorrow over the impact of its recent £16.7bn deal with Russia's Rosneft when it unveils its third quarter results.

State-backed Rosneft agreed to buy BP's 50% stake in its troubled TNK-BP joint venture for $17.1bn (£10.7bn) in cash and $9.7bn worth of Rosneft shares.

Investors have been left wondering how they will benefit from the deal, which will see BP grab a 19.75% stake in Rosneft as it becomes the world's biggest publicly traded oil company. Meanwhile, BP will count the cost of its far-reaching disposal plan as lower production triggers a 25% slide in quarterly profits.

BP is expected to report underlying replacement cost profit of £2.5bn in the three months to the end of September, a 25% drop on the same quarter last year.

BP is becoming an increasingly smaller company as it sells off large chunks of its business as part of its pledge to raise cash to pay the costs of the 2010 Deepwater Horizon disaster.

BT will be looking to calm investors with its second-quarter update on Thursday after it revealed weak sales to businesses and an under-pressure performance in crisis-hit Europe.

The telecoms giant is expected to report pre-tax profits of £595m for the three months to the end of the September, a 4% rise on the previous year, while revenues will slide 7% year-on-year to £4.5bn.

Shares in the company have fallen since it posted a 6% drop in revenues on a year earlier to £4.5bn for the first quarter as its Global Services division reported sharply lower corporate spending, reflecting tough conditions in Europe and the financial sector.

Elsewhere, rival Royal Dutch Shell will give its third-quarter update on Thursday and is also expected to reveal a rise in profits to $6.3bn quarter-on-quarter as it benefits from higher oil prices.