Daniel Jones, 59, is currently serving a seven-year prison sentence for his part in the Easter bank holiday weekend raid in April 2015, which saw a gang ransack 73 safe deposit boxes at the Hatton Garden Safe Deposit.
They used a drill to bore a hole in the vault wall, taking property worth up to £21m after a woman earlier this year claimed to have lost £7m in the raid, only realising it was missing after the trial of the men.
Jones has now admitted to attempting to break into a safe at the exclusive Chatila jewellery store in Old Bond Street, Mayfair on the August bank holiday weekend in 2010, according to the Evening Standard.
He pleaded guilty to conspiracy to commit burglary at Southwark Crown Court and will be sentenced at a later date.
It is believed around £1m worth of jewellery was stolen during the raid.
A second defendant, Terry Perkins, 68, of Enfield, has denied making off with goods worth more than £1m. A third Charles Matthews, 54, from Virginia Water, Surrey, denies one count of handling stolen goods.
Perkins and Matthew are due to stand trial on 27 February.