Parkes – chairman of entertainment agency Public Eye – is renowned for having had both Miller and Jude Law on her books during their high-profile break-up last year. Law is now represented by Premier PR CEO Sara Keene, while his ex-wife Sadie Frost is a Hackford Jones (HJ) client.
Deeley's previous publicist, HJ co-founder and director Simon Jones, advised her for seven years, a relationship that began when Jones was at Freud Communications. Deeley and HJ parted company last month.
Jones said it had been 'time for a change', because HJ is a UK-centred agency.
In the past two weeks HJ has won the UK account for US singer Hilary Duff, and has been signed up as Dancing on Ice presenter Holly Willoughby's first personal publicist.
Two months ago TV chef Jamie Oliver also signed up with Parkes, amid reports of plans for a US version of Jamie's School Dinners.