This is possible - but you need to check out the conditions of any funding you have very carefully as its likely it will be specific to one Uni/course and not transferable. Changing Unis mid-PhD is not common and usually only happens because a supervisor changes Unis and brings PhD students with them, or the PhDs are linked to funding money that the supervisor is transfering to another University.
Changing Unis because you aren't happy with current supervision/expertise is very rare (ie. you should have checked this out properly before you started there). If you are currently at a 'lower' Uni with lower expectations, its quite possible that a second Uni will not accept you - either because they are suspicious you are leaving for 'other reasons' (ie. you are a 'difficult' student) or that they aren't interested in research that has already started and they have to re-mould to fit their research priorities or 'higher standards'. Understandably Universities are not interested in 'academic tourists' who think they can get a place at a 'not very good' Uni and then trade up to something better. It suggests that the University brand-name is more important to you than your research.
Also, be aware that Cranfield is a research University only and funded by the British government to research defence and other 'government' type research projects. It is not a normal University and does not have thousands of students. It is very rare for anyone to be researching there unless they are on a specific funded studentship and most research there concentrates firmly on STEM type projects. You therefore will find it difficult, or impossible, to do a PhD in 'Management' there unless it allies with an existing project. Also, if you are an overseas student be aware that you might be subject to security restrictions.
You should email a prospective supervisor with basic details of a) your research, b) why you want to change Unis and c) details of any funding you have. Only if they want to take this any further (ie. they require a formal application with references) would you need to tell your current supervisor.