Wonky headstones that distressed grieving families and risked graveside injuries may finally be fixed.

The board responsible for Morden cemetery, which is jointly funded by Sutton and Merton councils, has pledged to tackle the problem of leaning headstones after years of complaints – but angry visitors said past promises have come to nothing.

Last week a report by Merton Council, which jointly funds the cemetery alongside Sutton Council, said it had been given quotes of about £130,000 for repair work in 2009 – but no action was taken. The problem is caused by subsidence of foundation beams designed to keep the headstones in place.

The report added masons were now refusing to put up headstones in the affected section, and existing ones could cause a danger in the near future. Carole Addis, whose mother Hilda Lissaman is buried at the cemetery, told council officers the state of her loved one’s grave was “very distressing”.

Mrs Addis, who lives in Dorset but grew up with her mother in Matlock Crescent, North Cheam, said the headstone has been propped up with unsightly pieces of masonry.

Susan Rubidge, whose parents are buried at the cemetery, said she reported the problem last year and was told in January the council would try to put things right, but had heard no news since.

She said: “My emails are now being ignored... My family attend our parents’ grave regularly. We will be very distressed and upset if we find the headstone lying on the ground damaged.”

The work would involve contacting families before headstones are temporarily removed, and new foundation beams laid. A Merton Council spokesman said the work would begin next month, as part of a wider programme of cemetery improvements.

Councillor Rod Scott said the board were committed to putting the problem right.

He said: “The next steps for us are to secure a contractor for both these works and for a proposed new landscape entrance, which would greatly improve the cemetery.”