It's the same doctor. I believe she's qualified in Australia, but lives/works in the UK. Her extremely word salad-heavy bio is here:
https://www.drolivialesslar.com/about and some of the UK clinics are referenced.
She clearly only works with private clinics, so she's not working for the UK National Health Service. Interestingly, she does not specifically mention her links to H4C, but there are pictures of her with Dr Tony and on the H4C IG.
Further (bold mine):
Dr Olivia works with innovative clinics and organisations worldwide. The major cities she works in are LA, London and Sydney. Her coordinating clinic is Cingulum Health - a neuro centre founded by renowned neurosurgeon Professor Charles Teo.
She curates personalised programs of synergistic adjuncts for neuroplasticity including transcranial magnetic stimulation, hyperbaric oxygen, photobiomodulation, PEMF, breathwork, physical rehab, dietary experiments with the gut-brain axis sin mind eg: keto, paleo and AIP, supplements, and nootropic peptides.
Dr Olivia is an Adjunct Senior Lecturer with The National Centre for Neuroimmunology and Emerging Diseases, a world-class research facility focusing on mechanisms of ME/CFS and long covid.
She splits her residency between London and the Gold Coast (Australia), and attends at least 20 conferences a year to keep abreast with advancements in medical theory and interventions. She has a burgeoning interest in Quantum Medicine and Consciousness.