The company said that Kensington and Chelsea had seen prices plummet by 16% since a peak in September 2014.
In Westminster it claimed there had been a fall of 22% between a peak in November and the end of May.
It blamed the fall on the new stamp duty regime, introduced in December, which penalises expensive properties.
Based on average prices, anyone buying a property in Kensington and Chelsea can now expect to pay more than Â£118,000 in stamp duty alone.
"This fall-off in the top tiers of the market has cooled activity levels too," said Adrian Gill, director of Reed Rains and Your Move estate agents, part of the LSL group.
He said the number of homes being sold in London as a whole had dropped by 16% in the year to April.
A wider survey by the Royal Institution of Chartered Surveyors (RICS) reported that the stock of houses per surveyor has fallen to its lowest level for at least 37 years.
However, prices in the London suburbs - and other parts of England and Wales - continued to hit new highs, said LSL.
According to its calculations, prices rose by 4.5% in the year to May, making the average cost of a home Â£277,178.
That is similar to estimates by the Office for National Statistics, but much higher than figures from Halifax and Nationwide.
Buyers of properties worth less than Â£937,000 now pay less in stamp duty than they used to.
Prices in England's smallest county - Rutland - rose by 23.8% over the year, while those in the Welsh county of Carmarthenshire went up by 16.4%.
Thirteen outer London boroughs saw prices hit new highs.
Previous figures from the Land Registry have suggested that prices in the suburbs across England and Wales have been taking off, including in parts of Manchester.
The separate RICS survey suggests prices in England and Wales could rise by as much as 25% over the next five years, due to the shortage of housing stock.
It said that, away from the South East, the strongest growth was expected in north-west England, as a result of the government's northern powerhouse initiative.
LSL's house price index is based on statistics released by the Land Registry, so includes cash sales.

Police said they were called to Peterhead Academy following an incident involving two boys on Monday afternoon.
The teenager was charged in connection with both possession of a knife and the assault.
He has been reported to the youth justice management unit.

John Harrington, 51, said he slapped Terry Hutchinson, 64, and it was not malicious but "playful".
Mr Hutchinson fell to the ground at West Herts Golf Club and suffered a brain injury, it is alleged.
Mr Harrington, of High Street in Redbourn, denies manslaughter at Luton Crown Court.
Mr Hutchinson had moved to Thailand where he married and returned to visit friends.
He was treated at the scene and taken to St Mary's Hospital in London, where he died on 27 May last year after three days of treatment.
Prosecutor Robert O'Sullivan QC said: "Mr Harrington did not intend to kill Terry Hutchinson. He is charged with manslaughter.
"The prosecution say he deliberately and unlawfully assaulted Mr Hutchinson and that assault was a significant cause of his death."
Mr Hutchinson had been drinking in the Red Lion in Bushey before being driven to Mr Harrington's pub, The Bull in Redbourn, the court heard.
Later another friend joined them and they were taken to the golf club where members of Mr Harrington's extended family were attending the wedding reception.
Mr O'Sullivan said: "There was a fair bit of banter on the part of Mr Harrington.
"What may have started out as drunken high spirits concluded with the defendant assaulting Mr Hutchinson with such force he went to the ground immediately and did not get up."
Mr Harrington told police: "I think I slapped him. I don't think I punched him. It was an open hand, not a fist. It was a playful slap."
The case continues.
House prices in the smartest parts of London have fallen by up to 22% since last Autumn, according to the property services group LSL.
[NEXT_CONCEPT]
A 14-year-old boy has been charged after allegedly being found with a knife at an Aberdeenshire school after an assault.
[NEXT_CONCEPT]
A pub landlord killed an old friend with a single punch on the way to a wedding reception near Watford in Hertfordshire, a court has heard.