I am a permanent resident in Germany and want to travel to the UK with my children who are on holidays. Do the parents have to apply for a UK visa?

Its part of the EU Nations so I believe you are fine..I am currently living in North America but I was an Italian resident (was born there so I am Italian) and traveling in the EU nations was always easy

But if you want more help, (something I found searching) You can check this out It deals with helping you get there easier

http://25af0zt2g9nhgrbfbgw1ek4q3f.hop.clickbank.net/?tid=BOTOTONB52

Anyways,  safe travels.