Sorry, but PhD is a doctorate - a person with a doctorate is entitled to call themselves a ‘doctor’. It means that you have studied at a specific and very high level above that of a bachelor or masters degree.
In the US upon completing training a medical doctor has an MD (ie is a Doctor of Medicine). In the UK, however, most medical doctors do NOT actually have a ‘doctorate’ - in stead they have a Bachelor degree in Medicine and a second bachelor degree in surgery (MB BChir or MBBS), hence they need to go on to further training before qualifying as a practicing physician - which is what they used to be called.
It is only in recent decades that ‘doctor’ has been perceived by the general public to exclusively denote a medical qualification - and is, therefore, erroneous. Moreover, most specialists cannot wait to dump the title of ‘Dr’ and become Mr (or Mrs) as they progress to seniority due to professional snobbery.
If you have a PhD in a specialist area of cancer research, for example, why the hell shouldn’t you be able to call yourself ‘doctor’? Your expertise will far outstrip that of a GP prescribing lotion for your eczema!
Disclaimer - I am entering the final year of my PhD, it’s been 6 years of study and slog to get where I am, so yes, I will absolutely be using ‘doctor’ in correspondence, both personally and professionally. And having bankrolled it, my husband will be seriously fucked off if I don’t.