I am attending a conference in the ExCel in London and am flying in that morning. The best value flights are all flying into Southend airport which I hadn't heard of before so I am wondering how long it takes to get into the centre of London from there and what is the most convenient way to get there?
There are lots of trains between Southend Airport and London Liverpool Street, eg see this listing for a Monday morning. Journey time is around 1 hour, and it's direct to Liverpool Street station. (Liverpool Street Station is located close to the City of London, but about 20-30 minutes to some of the common tourist sites in the West End and Westminster)
Cost wise, depends on the time of day. Currently (2013), an anytime single is £15.70 - that's valid on any train. A super off-peak single with a Network Railcard (or similar) on a weekend is £9.85.
For the ExCel, you probably want to go to Customs House station on the DLR. That's only just over 1 hour, with a change to the DLR at Stratford. (Timetable for a Monday morning for an example). That's actually slightly cheaper than going into London Liverpool Street, at £14.20 for an Anytime Single, down to £9.05 for an off-peak with a suitable railcard.
I've never flown to this airport myself, but from what you get on the Internet, it seems that this airport is well connected to London Liverpool Street Station (up to eight trains per hour at busy times), and it takes just under one hour to get there. Pity that on the site there is no indication as to how much a ticket to London costs...
Apparently, there is no other public transport which may take you to London, as both buses and coaches may take you to Stansted, but there again you should rely on the train service. Of course, you may consider hiring a car or catching a cab, but the airport is 40 miles east of central London, so I guess it might be a bit expensive.