Bagage allowance and number of pieces of luggage: you will need to check with your airline company. Each airline has its own policy and not following the rule could cost you a lot of money and trouble at the airport.
Weather forecast (of course!): you can the weather that is expected by clicking here. This will determine your choice of clothing.
Activities in London: in principle you might opt for casual clothes and a comfortable pair of shoes. Even to go to the opera or concert, people have a tendency to dress less than in the past but if you are planning to have some 'posh' events, be prepared to dress up. Jeans and sport shoes can be forbiddent in some place like private clubs or for a high tea at the Ritz.