The Mesh Oversight Group report also said complications caused by the implants should be recorded so that experts fully understood the risks.
Vaginal mesh implants are used to treat stress urinary incontinence and pelvic organ prolapse.
But some women said they left them in permanent pain and unable to walk.
The research - seen exclusively by the BBC's Victoria Derbyshire programme - aims to address concerns over the use of mesh devices.
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Prof Keith Willett, who wrote the foreword to the report, said it contained three key recommendations:
The report says: "Adverse events involving mesh as a medical device must be reported and clinicians must bear this responsibility."
It also says surgeons undertaking surgery for stress urinary incontinence "must be able to demonstrate they are performing these operations regularly".
It says that where a mesh is being used to treat pelvic organ prolapse "this should not be offered routinely for the first surgical intervention".
The plastic meshes are made of polypropylene - a material also used to make certain drinks bottles - and are manufactured by many different companies.
They are used to ease incontinence and to support organs such as the vagina, uterus, bowel, bladder or urethra which have prolapsed after childbirth.
The  MHRA says, for the majority of women, the use of vaginal mesh implants is safe and effective.
But some can cut into the vagina, causing severe discomfort.
Currently in the UK, there are around 100 types of vaginal mesh implants.
An NHS England report on vaginal mesh implants has recommended better support and communication between patients and doctors over the devices.