Latest Adoption Leadership Board data shows that 1,060 children were adopted in the three-month period between July and September 2016, down from 1,070 in the quarter before and from 1,160 between January and March 2016.
The number of new placement orders has fallen from 1,630 between July and September 2013 to 830 in the same period of 2016. Between April and June 2016 the courts granted 1,020 placement orders.
The falls follow a downward trend for both measures in recent years which has been linked to the impact of the September 2013 Re B-S judgement, which indicated that local authorities need to show the courts that all alternatives to adoption were considered before seeking an adoption order.
A number of attempts to address the situation have been made in recent years.
Andy Elvin, chief executive of fostering and adoption charity The Adolescent and Children's Trust said the decline is now more likely to be due to the impact of special guardianship orders (SGOs), the use of which have been increasing in recent years.
"I don't think that Re B-S is still playing out," Elvin said.
"These figures reflect the continued rise of SGOs [granted to] family members and, in reality, SGOs and adoption figures should be taken together alongside long-term fostering to show how well we are achieving permanency for vulnerable children.
"I remain concerned that we give SGO assessments enough time to be of sufficient depth and rigour to ensure that breakdown rates are low.
"There is no ‘right' number of adoptions, we need to make sure that, case by case, we are getting permanency decisions right for children."
The data also shows that fewer children are waiting to be adopted.
As of 30 September 2016 there were 2,030 children and young people with placement orders waiting for an adoptive family, including 590 who have been in care for at least 18 months. This compares with 2,190 as of 30 June 2016.
It is also taking less time for would-be adopters to be approved, with 29 per cent being approved within six months of registration compared with a quarter in the January to March 2016.
However, the speed at which adopters are matched with children is still declining. In January to March 2014, 80 per cent matches occurred within six months of adopters being approved, compared with 43 per cent in July to September 2016.
Adoption UK chief executive Sue Armstrong Brown said: "Whilst there is much to celebrate in these figures, there's also a lot more to do.
"The fact that children are spending less time in care before being adopted, down by four months - from 22 months to 18 months - is really encouraging.
"We know that the sooner children find permanence in their adoptive home, back with their birth families, or in long-term care plans, the better their outcomes.
"We need to keep a close eye, however, on the time it is taking to approve adopters, and gain a better understanding of why it's taking relatively longer to gain approved adopter status now, than it was in 2013/14.
"The decline in the number of adopters means that this autumn, for the first time, the number of children needing an adoptive home will outnumber those coming forward to provide that home.
"Clearly we need to do more to recruit potential adopters, as well as speed up approvals, whilst retaining the rigorous assessment that's part of that process."