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.
What's the issue with mesh implants?
Mesh implants 'as dangerous as asbestos'
Faulty implants end women's sex life
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.

Media playback is not supported on this device
Phelan, 53, was promoted from assistant boss to caretaker manager when Steve Bruce resigned in July.
Despite a threadbare squad, he has a 100% Premier League record with wins over Leicester and Swansea.
"He can handle the situation at Hull and the players are playing for him," Neville told BBC's Match of the Day.
Phelan chose not to make a substitution last week and only made one in the 2-0 victory against Swansea, bringing on Shaun Maloney, who scored the opening goal.
Hull are yet to make their first signing of the summer transfer window, despite the departure of several members of last season's promotion-winning squad and a long injury list.
Phelan worked under Sir Alex Ferguson for 12 years, having served as a first-team coach from 2001 and assistant manager from 2008-2013.
Neville said that experience means he is equipped to deal with the pressure at Hull.
If you talk about someone who deserves the opportunity then it's Mick Phelan
"He's done an incredible job so far," added Neville, who was part of the United squad when Phelan was on the coaching staff.
"Mick's galvanised that team spirit. They've had a horrendous pre-season. They've got no squad and he's had kids on the bench.
"If you talk about someone who deserves the opportunity then it's Mick Phelan."
Hull's win over Swansea, which took them third in the table, was sealed by an injury-time goal from Abel Hernandez.
The away fans at the Liberty Stadium chanted 'we want Phelan in' but he knows he must continue to win matches if he is to get the job on a full-time basis.
He said: "It was nice to hear them singing that - it's better than hearing them singing 'we want Phelan out'.
"I think everyone knows we have decisions to make on my future, the future of the staff and the ownership."
An NHS England report on vaginal mesh implants has recommended better support and communication between patients and doctors over the devices.
[NEXT_CONCEPT]
Hull City should give Mike Phelan the manager's job on a full-time basis, former England defender Phil Neville told BBC's Match of the Day.