Unless you're aiming for a PhD I don't think the standalone masters route is likely to add much. Even if you are I don't think it's really necessary unless the specific area you want to research has better supervisors at those unis for the masters thesis/dissertation.
If this is just to get the name of Oxford or Imperial on your CV I don't think that's going to matter at all unless applying for management consulting or investment banking roles. If you actually want to work on engineering I don't think it matters...Southampton has a good engineering programme anyway.