I have a Dr.rer.nat from Germany but currently I am working for an institute in the United Kingdom. Is it legal or acceptable to continue to use the title Dr.rer.nat (First Name) (Last name) in the UK or do I need to change it to (First Name) (Last name), (Ph.D)?
It is certainly legal to refer to yourself by the title you would use in Germany - few titles are actually legally controlled in the UK - and I would say it is also acceptable. However, I would suggest that is advisable to use the normal UK convention so that your audience understands what your title means without you needing to explain.
I would therefore use Dr user23530 rather than Dr.rer.nat user23530.