The problem with the London shows is that there is now a very keen interest from press and buyers who would normally skip the week in favour of New York, Milan, and Paris. Unfortunaely due to the nature and budget of British designers they tend not to show in large venues which makes gaining access very difficult even for genuine industry figures. I remember a friend of mine Natalie Theo the fashion editor for the Daily Mail, telling me she wasn't even invited to Gareth Pugh's Spring/Summer 2008 show although she works for Britains highest circulated newspaper.
The best advice I can give is contact Pr directly. Choose a discreet show which is unlikely to be attended by anyone of prominence (The company will know this and will look for anyway possible to fill the show) Explain to them your reasoning for wanting to see the show. Here honesty is the best policy, but try and think of a way your prescence could be of benefit to the designer or the company, e.g You saw their last collection and were impressed by the clothes therefore would like to come and see the show with the attitude to buying pieces from the collection as a private buyer (you never know you might fall in love with something so this isn't entirely false.) This technique can often work well.
To attempt a bigger show can be an entirely different scenario, I personally wouldn't recommend it unless you have a ticket (or the balls to be interogated infront of the entourage of fashion editors from Conde Nast) Either contact the PR company for work or network until you meet a man who sold milk to the boyfriend of Christopher Kanes Sister (you never know)
In terms of fashion week events, parties are far worse than shows, and will almost be like hitting a brick wall for most of you. More often than not an invitation to a show equals an invitation to the after party, but if your not lucky enough to get one of these then your best hope is standing around outside the venue to see if you can sweettalk your way in.
For London Fashion Week it is possible to get into the various exhibitions around town, but it is essential you gain a pass. This isn't always possible, but I know certainly that for the tents at the natural history museum you need a pass from the british fashion council which is only distributed by them, if you ring the BFC and explain to them for example you are a student and would be very interested in attending they will be helpful and numbers permitting will grant you a pass which is emailed to you as a barcode then exchnged for a badge at the door when your identification has been checked. It's also beneficial to do this as once you have this pass you will be looked at more seriously if you do decide to attempt a crash at a larger show. Similary at the Royal Academy for the on/off exhibition you will need a pass but I have seen people enter before just by explaing their situation and the gaurds are usually helpful (Remember although they are trained for these sorts of events, they aren't fashion people and therefore do not think or behave like fashion people, making it a lot easier to befriend them.) I'm not sure how you would obtain one of these as I am just sent one automatically but I see no harm in ringing them to see.
If you just want a taste of the fashion week madness just get to any of the cities and go have a look, yeh you may not get into the shows but it's still fun to go and people watch and I know certainly in London watch some of the incredible things people are wearing! Places like Harvey Nichols have large screens in there eateries for customers to watch the shows live, and Topshop give away London fashion week merchandise like free bottled water in their stores, and if anything it's just an excuse to go do some extra shopping in time for the ne season! I hope this can be of some help!