The child protection section of Bath and North East Somerset Council has been graded as "adequate" after an unannounced Ofsted inspection.
Inspectors, who arrived just one hour after a telephone call to the local authority, spent more than a week looking into the way vulnerable children and young people in the area are kept safe.
Their report shows that although the council is meeting the minimum requirements, more needs to be done to improve services in the future.
It highlighted the need to improve the quality and effectiveness of support young people receive and make sure that cases are dealt with more quickly.
The inspectors discovered that a "very large rise" in contacts and referrals, combined with staffing pressures, since December last year meant there were delays of up to one month in the allocation for assessment of a "significant number" of cases.
This had led to high caseloads for some social workers, however the team did not identify any children who were at risk of immediate harm.
Councillor Dine Romero, B&NES cabinet member for early years, children and youth, welcomed the report and said the local authority was already looking at ways to improve services.
She said: "I am pleased with the inspection judgements made as it demonstrates our commitment to protect children and young people.
"Ofsted were impressed with the improvements made over the last year and are satisfied that B&NES Council, with its partners, is taking measures to improve services further."
However, opposition councillors have raised concerns about planned cuts to children's services in light of the Ofsted report.
Conservatives have said it calls into question budget reductions of up to 50 per cent at the council's children's centres.
Councillor Anthony Clarke (Con, Lansdown) said: "Whilst the Ofsted rating of 'adequate' should provide reassurance that B&NES is providing the services it should do at the level expected, there clearly remains room for improvement.
"This has to call into question some of the cutbacks B&NES is planning to make to children's services in the coming years, particularly at children's centres which are often able to pick up pick up potentially challenging situations early."Click here to find the full report.
