It's always a pain getting to Heathrow from SE1, I used a new shuttle service from National coaches, half the price or less than a minicab and a lot more comfy, you have to leave early but at least it's door to door. http://www.dot2.com/Home.aspx. No connection etc.
I was never able to get the website to work, but I did call and have booked myself on one of the shuttles. £20 for one way from my flat in SE1 to Heathrow. I have to leave about an hour earlier than otherwise (6:30 am).
I could have booked the return but have left it for now. They told me I can go to their desk in the terminal when I fly back in to Heathrow, and if I tell them my confirmation number from the first shuttle, I'll get the return shuttle for £18.