The problem with the extending the taxiway is the fact that it would have to be parallel to the runway (safeguarding issues). The problem with that is that Mitchell Way turns in towards the runway too. Therefore you have to straighten that out, and to do that do SOU own the land next to the railway station, would moving the road affect the railway track etc. You'd have to move the Glidepath to the other side...etc.. it all mounts up to a big job and a big cost.
All the above could be avoided with a parallel taxiway to the east of the runway, running from a new taxiway/runway crossing point at the northern end of the current main apron and then north-east up to the 20 threshold. The SOU Masterplan included this and also aircraft parking stands in the north-east corner of the airfield.
http://www.southamptonairport.com/st...e-SOU_maps.pdf
Granted, runway crossing would be needed, but not back-tracking for 20, and all the issues Pottwiddler mentions above would be avoided?