The Local Government Association warns that patients could face longer waiting times.
But the latest data shows diagnoses of sexually transmitted infections (STIs) have fallen in the past year.
The government said more than £16bn was being invested in public health.
Responsibility for public health in England has rested with local councils since 2013 – but the Local Government Association says it has not been given adequate resources to run proper services.
It points to budget cuts of more than £500m – nearly 10% – over the past two years.
The overall public health budget is £3.4bn for 2017-18 and councils spend around £600m a year on sexual health services.
With the number of new attendances at sexual health clinics up by around 25% – from 1,941,801 in 2012 to 2,456,779 in 2016 – councils say they are facing particular pressure.
However, there is some positive news – new diagnoses of STIs, such as gonorrhea, chlamydia and genital warts, fell by 4% from 2015-16.
Chlamydia is the most common STI in the UK and is easily passed on during sex. It can be tested for by providing a urine sample or a vaginal swab.
Council leaders say it is good news more people are taking responsibility for their sexual health, but they warn that higher numbers are turning up at clinics and putting a strain on resources.
The LGA says patients could face a poorer quality service and wait longer for tests and treatment if additional funding is not provided.
Cllr Izzi Seccombe, chairman of the LGA’s Community Wellbeing Board, said: “The reduction in public health funding could also compound problems further and impact on councils’ ability to meet demand and respond to unforeseen outbreaks.”
She added: “It is obviously good news that diagnoses of sexually transmitted infections are down, but sexual health services are now reaching a tipping point where it will be extremely challenging to maintain this progress.
“Once again this is an example of councils inheriting the responsibility of public health when it was transferred from the NHS in 2013, but without the necessary resources to deliver services.”
A Department of Health spokesman said: “Sexually transmitted infections, including HIV, are continuing to fall and over the current spending period we will invest more than £16bn in local government public health services.”
It added that NHS England and Public Health England would soon be launching a “major pioneering ” trial, providing the HIV prevention drug PrEP to more than 10,000 people.