You should be more specific... What size account? Experience? Remote/on-site? Are you looking for a firm based in the UK or one that is just able to trade UK stocks and based elsewhere? And also where you're based.
This is not correct. You can get around the stamp duty by trading CFDs or by holding a security for less than a month.
If you are an exchange member and hold the security for less than 28 days. There are different types of membership and I believe LSE has recently made it easier to become a member for competitive reasons. Or if you qualify for "Intermediary Relief" then there is no holding period. See also http://www.londonstockexchange.com/traders-and-brokers/membership/faqs/general-faq/general-faqs.htm
Can individuals become members of the Exchange? Private persons can not trade directly on the London Stock Exchange and to become a member, you must meet a number of requirementâs which can be found above and relate to authorised/exempt firms not approved/exempt individuals. If you wish to begin trading as a private investor you should contact one of the London Stock Exchange's retail member firms.