I don't think it would make you stand out, you would be better off doing a mechanical engineering MEng at one of the universities with a reputation for getting people into F1 (Imperial's one of them, I'm pretty sure there are other ones which don't have as high entry requirements but I can't think of them right now as it's not really my area of interest).
One of the important things for getting into something like F1 is doing Formula Student, and a lot of Formula Student teams restrict entry to engineers only (and often just mechanical and occasionally aerospace engineers can join). So if you're doing Physics you would only be able to do 1 year of formula student, if that as again some teams will only recruit 1st years (and I don't know if there are restrictions on postgrads working on FS), compared to 4 years if you did engineering as your undergrad.
Also by doing just an MSc in engineering you miss out on a lot of the content that someone with a BEng or MEng would learn, and you may be limited in what MSc courses you can take as nowadays quite a few are asking for your previous degree to consist majoritively of engineering modules or something to that effect.