From my experience at Brunel (doing core Mechanical Engineering, but knowing plenty of people who did Motorsport) I'd say the best thing to do would be to do core. Motorsport Engineering degrees are less well known, and will only ever have ANY credibility (if it gets any) in motorsport. On the off chance that motorsport doesn't work out I think lots of employers in non-motorsport engineering would be put off by the idea of 'specialist' degrees.
Bear in mind the worlds most successful engineers in F1 have either core Mech. Eng. degrees (at Masters level, which is why you are doing a 4 year course), or Aero. Eng degrees.
I'd also say don't be too worried about doing work experience. If you are in the lucky 10% who get a place they enjoy you'll benefit wonderfully, but if you, like most, get a shitty job making coffee for the professionals, and doing crappy jobs all day long, then it's more likely to put you off engineering than give you any valid experience. By all means apply, but if you can't find anything you don't want to do then just go straight into your final year.
And avoid Chris Brown at all costs, becuase he is an arse in the worst meaning of the word.