In its interim management statement it shows its net UK mortgage balances grew by £2.6bn in Q3 2010, up 6% from Q2 2010.
It says that this reflects the roll off of a large number of customers from fixed-term mortgage deals, as well as greater competition in the market.
And its market share for gross mortgage lending remained high, at 14%, in Q3.
It says scceptance rates remain high at approximately 90%, and it continues to offer a wide range of mortgage products up to 90% LTV.
RBS says it continues to support the first time buyer market, helping more than 8,000 customers to move into their first home during Q3 2010.
With net lending of £5.8bn in the seven months March-September 2010, RBS remains on course to achieve its £8 billion mortgage lending target for the March 2010 to February 2011 period.
RBS is reporting an operating loss of £1.4bn in Q3 2010, compared to a £1.2bn profit in the previous quarter.
The bank says the loss is down to the fair value of its own debt, which stands at £858m, which wipes out the operating profit of £726m.
The attributable loss stands at £1,1bn for Q3, including an £825m APS fine.
RBS says wholesale funding market conditions improved significantly during the quarter and its public and private issuance totaled £18bn in the first half of 2010.
This included RBS’s second covered bond and its first residential mortgage-backed securities public issuance since 2007.
Stephen Hester, chief executive of RBS, says: “Our third quarter results demonstrate that we continue to make good progress in our recovery. We are delivering what we set out to achieve.
“The Core Bank is becoming stronger. As we focus on serving customers better, profitability is also improving and rebalancing towards a more sustainable mix of business contributions.
“While economic challenges, especially interest rate-driven, and regulatory costs will impact the level of improvements targeted and their speed, RBS remains focused on achieving balanced progress across all our key objectives.”
The value of mortgage arrears increase by £11m in three months to September but remained at 0.2% of the mortgage book but total impairment charges fell by 40% to £1.95bn.
The core tier one capital ratio is at 10.2%, which is well above the Basel II requirements of 7%.