Applying for an MPhil or PhD in Computer Science at Cambridge University
The MPhil in Advanced Computer Science is designed as a preparation course for the PhD, so yes, it is absolutely normal to apply for the MPhil with the intention to apply for a PhD while there. Being there also gives you the opportunity to get to know your potential PhD supervisor better. And you can get support from the Computer Lab and your college during the application process.

The degree itself is comparable to a single year of a two year master's programme. I recommend not to just apply "to Cambridge" but to spot the group or even the advisor you would like to work with. The Computer Lab is great for some fields, but not ideal for others, because as any department they cannot have a research group on every subject.