We have pretty much the same data protection/privacy laws in the UK as in EU countries, from our time in the EU. The only real difference is in how those laws are interpreted in the different countries. In UK there is no problem unless the video is published, and if using a camera at a tourist/public site, the problems arise only if an individual becomes the subject of the video rather than them just being identifiable, and even then it is hard to get any sort of conviction. For a dashcam, the rules are probably the same although I don't think it has been properly tested in court yet. Business and home CCTV recordings however seem to be being treated somewhat differently since the purpose of such a system is clearly for security and nothing else, and so under the data protection act you are not supposed to keep security recordings for longer than necessary, and you have a duty to keep them secure. Potentially the same rules could be applied to dashcams if there was a bad court case which decided that, however I use a dashcam to record my trips as a tourist, so the rules should stay the same as for DSLRs and phone cameras.
There is a Tesla dashcam function *Sentry Mode" which does record within the car. Not sure what the legality of using it is in Portugal, but I think it only keeps one hour, and in some places may only record if it detects someone at the vehicle, so it may comply with CCTV laws. In Portugal you will not be allowed to publish the recorded footage without blurring plates and faces like Google Street View does.