Well, the public transport share to and from UK airports varies a lot. In the 2010 CAA Airport Survey for 12 English airports the public share was as follows:
London City = 52.4%
Stansted = 47.8%
Gatwick = 40.4%
Heathrow = 39.2%
Luton = 32.8%
Birmingham = 24.9%
Liverpool = 17.9%
Manchester = 13.6%
East Midlands = 8.7%
Doncaster = 8.5%
Leeds Bradford = 6.5%
Humberside = 0.5%
The three best in Europe the same year had the following public share:
Oslo, Norway = 67%
Zurich, Switzerland = 59%
Copenhagen, Denmark = 57%
All three of these European airports are sitting on top of a hight speed rail link in to the city centre, and with a travel time of only 11 to 19 minutes.
I've flown to and/or from all the twelve English airport (and Southend too), and it's not without reason that these low public transports shares exists. For example, to give the railway service from Liverpool Street to Stansted the name Stansted Express is an insult - 46 minutes to cover only 37 miles. With at least 9 more minutes to reach Southend Airport and that with only 2 miles more than to Stansted, I don't think the train link will be a winner. I think you may struggle to reach 10% for the railway use at Southend. I hope the onsite parking is large enough.