The new rules - known as the Mortgage Market Review (MMR) - came into effect at the end of April.
It meant home loan applicants had to give more details about their income and outgoings during longer mortgage application interviews.
Lenders are reporting a steady rise in first-time buyers despite the changes.
There were 28,600 loans given to first-time buyers in June, a rise of 7.1% on the previous month and 18.7% higher than in June 2013, according to the Council of Mortgage Lenders (CML).
In the second quarter of the year, first-time buyers borrowed an average of Â£122,000, up from Â£118,750 in the first three months of the year. They typically borrowed 3.46 times their income, up from 3.43 times their income in the previous quarter.
"For the second month running since new FCA rules took effect, lending characteristics remain similar to the market beforehand," said Paul Smee, director general of the CML.
"We now feel confident that, as we would hope, the MMR effect is more gentle dampener than hard brake."
Under the new rules, potential borrowers have to give evidence to the lender about the funds in their personal budget.
This could include regular payments for haircuts, gambling and club subscriptions and deliveries, to holidays, travel season tickets and childcare.
Borrowers might also be expected to say if their financial position is expected to change. That could include any predicted changes in income or working hours, but might also include any plans to have children in the near future.
Some brokers and estate agents have said the process of a mortgage application can take longer now.
"Those who are lucky enough to be buying with cash have the best choice in the marketplace. The new mortgage rules will hamper those who need to borrow, as they are constrained by what they can afford and the length of time it will take," said Hugo Thistlethwayte, managing director of buying agency Prime Purchase.
Overall, the CML said that there were 60,500 mortgages advanced for house purchases in June. This was a rise of 5.4% on the previous month and 14.6% up on June 2013.
Low interest rates and a recovering economy have both assisted the pick-up in the housing market in many parts of the country, commentators have said.
A survey by Aviva, published on Monday, suggested that people buying a home in the last year typically spent 33 minutes looking around the property before making an offer.
Enter your details into the calculator to find out:
Find out more about this calculator

The former Sierra Leone tactician was dismissed on Thursday after 15 months in-charge of Amavubi.
McKinstry said he was "surprised and disappointed" and the reasons "had not been made fully clear" to him.
McKinstry took over the Rwanda job from Englishman Stephen Constantine who stepped down in March 2015.
The Northern Irishman then led Rwanda to the quarter final stage of the 2016 Africa Nations Championship that they hosted.
He also led the team to the runner-up spot in the 2015 Cecafa Senior Challenge Cup in Addis Ababa, Ethiopia.
"The specific reasons behind the decision have not been made fully clear to me given our performance to date, I am therefore both surprised and disappointed by the announcement today, and that myself and the team will not be able to finish what we started," he said.
The 30-year old coach managed to record 11 wins, two draws and a dozen defeats in the 25 games he was in charge of Rwanda.
According to the Rwanda FA, McKinstry was sacked because he did not achieve some of the targets that had been set for him.
The FA announced former international Jimmy Mulisa, who had been McKinstry's assistant, as Rwanda's interim coach.
Mulisa was a key part of the Amavubi side that featured in the country's first and only Africa Cup of Nations finals in Tunisia in 2004.
New affordability checks have only put a "gentle dampener" on the UK mortgage market during their first months of operation, lenders say.
[NEXT_CONCEPT]
Northern Ireland-born Johnny McKinstry has expressed his surprise after he was sacked as head coach of Rwanda's national team.