What is the advantage of doing an integrated Masters course over a Bachelors and then Masters? (UK.)
An integrated masters such as an MPhys is an enhanced undergraduate degree where the final year will include level 7 courses and a substantial project. It will typically be accredited and meet the academic requirements for registration for chartered status (CPhys in this case).

An MSc is a postgraduate degree also with a substantial project and level 7 courses. It will often be more specialised in nature than an undergraduate degree and may or may not be accredited such that it will add the necessary academic requirements for chartered status if the student also has completed an accredited BSc.

In the UK there will typically be a difference in fees between the two cases and there is currently (although this may change or may even have changed already - you should check) a difference in funding available. Government backed student loans have only been available for undergraduate degrees.

For engineers in industry I do think that generally the integrated Masters is looked at more highly but of course it  depends on the institution. If you goal is to get chartered status then I would advise the integrated Masters rather than a separate MSc provided you are staying in the UK. If you go abroad the separate postgraduate MSc is understood better and so probably easier to have accepted.