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Most banks offer brokerage accounts, just check with whoever you're with (you have to go through a broker to buy/sell btw). I'd not advise buying shares just because they've plummeted in value though, unless there's absolutely no reason for their doing so.
Depends if you know what you're doing or if you don't. If you know what you're doing and understand why you're buying this particular company (especially seeing as NR are in some strfe) then go for a straight discount broker. Online ones are generally cheaper.
If you want advice and want to read stock analysis and stock research then look for a full fledged brokerage service. I'm not sure about UK but the big ones in US are guys like Merrill Lynch and Morgan Stanley. Try the big banks like Barclays or HSBC for services.
Stocktrade (www.stocktrade.co.uk, based in Edinburgh) and BMO (www.bmoinvestorline.com, based in Montreal) are two of the best brokers I've ever dealt with. Also, I would strongly advise against using Citigroup.
It's quite possible that you will need to set up an account with them if you do use them though.
I use Hargreaves-Landsdown h-l. They are slightly more expensive than hoodless but have a better rep. Also good if you want to buy funds at any time, as they refund almost all the charges that the funds make (pass on their commission to you basically).
I wouldn't touch NR at the moment personally. The city may have panicked a little with the 30% drop on the BoE news, but that's starting to look reasonable now that all their savers are withdrawing their funds. There could easily be further big falls yet. Only invest what you can afford to lose etc.