If you file a combined mark consisting of a logo, name, and slogan, such registration implies that you should use all the elements together in a way depicted in the application.
As for the level of protection, if you file a combined mark, all of the dominant elements of the mark in isolation are implicitly protected. If one or more elements of the mark lack a sufficient level of uniqueness and can be considered generic or descriptive, they can be used freely by any third parties.
Imagine you have a brand name called "Car wash services". You decide to file for a combined mark in the UK, including the words "Car wash services", to which you apply a font (i.e. stylisation). Underneath the brand name, you include a unique custom logo. You also add a tagline, "The best carwash out there".
If a third party uses the name "Car wash services," they do not infringe on your trademark, as you cannot claim exclusive rights to a generic term. However, if someone copies the brand name with your logo in the UK, you can claim infringement. As for the slogan, it is only protected if used with other dominant elements of your mark. Anyone can claim they are the "best carwash out there".