About 60 families were unable to get their child's remains because of poor training and out-of-date equipment at council-owned Emstrey Crematorium, Shrewsbury, between 1996 and 2012.
Lawyers believe the crematorium breached the Human Rights Act.
The council said it was liaising with its insurers.
A spokesman for the authority said: "Shropshire Council confirms it has received a letter of notification in respect of Emstrey Crematorium and this has been passed to the council's insurers, who will deal with the matter confidentially in the usual way."
If the legal challenge is successful, it could pave the way for action against crematoriums across the UK where other families were not given their child's ashes.
A Freedom of Information inquiry by the BBC last year found the ashes of more than 1,000 babies were not handed to their parents between 2008 and 2013.
The scandal in Shropshire came to light following a BBC Radio Shropshire investigation.
The lawyers are representing families who have joined the campaign group Action for Ashes.
In June, an independent inquiry into what happened in Shropshire ruled a national inspector should be created for crematoriums.

Meaning "to watch a large number of television programmes (especially all the shows from one series) in succession", it reflects a marked change in viewing habits, due to subscription services like Netflix.
Lexicographers noticed that its usage was up 200% on 2014.
Other entries include dadbod, ghosting and clean eating.
Helen Newstead, Head of Language Content at Collins, said: "The rise in usage of 'binge-watch' is clearly linked to the biggest sea change in our viewing habits since the advent of the video recorder nearly 40 years ago.
"It's not uncommon for viewers to binge-watch a whole season of programmes such as House of Cards or Breaking Bad in just a couple of evenings - something that, in the past, would have taken months - then discuss their binge-watching on social media."
Those partaking in binge-watching run the risk of dadbod, one of ten in the word of the year list.
Referring to an untoned and slightly plump male physique, dadbod is not without its admirers, with actors like Seth Rogen and Leonardo DiCaprio fitting the purported brief.
"Once again, the list of Collins' Words of the Year offers a fascinating snapshot of the ever-changing English language," said Newstead.
Those words that remain popular could be included in the next print edition of the Collins English Dictionary, due in 2018.

John Biggadike died when he fell while in the hoist and was impaled on a metal post at Boston Pilgrim Hospital.
At Lincoln Crown Court, the prosecution alleged hospital staff were not adequately trained and had wrongly removed a knee support pad.
United Lincolnshire Hospitals NHS Trust denies breaching health and safety regulations.
Mr Biggadike was receiving physiotherapy at the hospital ahead of being discharged in April 2012 when the incident happened.
More stories from around Lincolnshire
The defence suggest Mr Biggadike's death was not caused by failings in training, but by a failure to act after a previous "serious incident" with a hoist at a hospital in Leicester in 2007.
Jurors heard evidence from Sarah Vincent, representing the Medicines and Healthcare products Regulatory Agency (MHRA).
Mrs Vincent admitted the Leicester incident was "serious" but conceded the subsequent MHRA investigation was limited to questioning the hoist manufacturer's own investigation and making sure the hospital trust had instructions for using the hoist.
United Lincolnshire Hospitals NHS Trust denies breach of health and safety regulations by exposing non-employees to risk by failing to train, supervise and monitor its employees in relation to the safe use of the lifting hoist on dates between July 2001 and April 2012.
The trial continues.
Lawyers representing families in the baby ashes scandal have said they are to take legal action against Shropshire Council.
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Collins English Dictionary has chosen binge-watch as its 2015 Word of the Year.
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Instructions for a hoist involved in the death of a hospital patient were not comprehensive, a court has heard.