Employment in the UK and Germany (London)

Good afternoon everyone,
does anybody have experience with tax and social security issues when working both in Germany and in the UK for a British Company? I know that there is a double taxation agreement but I would love to know how (complicated) this works in reality.
If I work in the UK 3 days a week and 2 days in Germany, is it possible to have medical insurance in both countries? If so, how expensive can that be?
It would be great if someone could share his/her experiences.
Thanks in advance!
Paulina