I totally agree with SS. Not wanting to shatter your hopes but this is not a good time to be considering a career move into banking. At 28 with no relevant experience, it wouldn't be a straightforward move at the best of times but right now, you're facing an uphill battle up a potentially vertical slope. Most banks have hiring freezes and/or have been making major job cuts, and as SS says, rumours are that there are more cuts to come in 2012. For those that already have jobs in banking, there is no job security at all. I have colleagues who were given 15 mins notice to leave the office when they were cut last month. No farewells, no advanced warning.....it's brutal right now. Not an industry to aspire to joining.
Just to add, it's a nice sentiment that you're willing to work for free in the afternoons but "leading banks" don't really work like that. There are all sorts of legal and compliance implications just to give someone system/building access, let alone the internal costs etc that are incurred. It's not just about salary. Seems a little naive of you.
Are you sure banking is really the right industry for you? Apologies if this comes across as being negative (but there's only so far I can dress up the message) but you will need to be VERY switched on to get into this industry, especially in this economic climate and especially when you've taken 5 years since graduating to work out you want to get into banking. A year or two you could probably get away with, but 5 years? You'd better have a VERY strong answer (and even with this, some firms will just ditch your resume straight away anyway). You'd effectively be applying at graduate trainee level which is beyond competitive (and again, most big firms have been reducing their graduate schemes) and to add to that, you'll have to justify why it's taken you so long etc etc. Saying you find the business news interesting is not going to cut it. You need to demonstrate you have something special to offer, whether it being outstanding qualifications (and by that I mean top of class, prizes, first class degree etc) and/or outstanding extra-curricular activities.
I assume you don't need a work visa?
Sorry for not being able to be more positive. Suggest you gave the grad schemes a go but make sure you are fully prepared for some very tough questions...and a very tough industry.