I have an EI flight using Avios as well. You will need to call the Executive Club and ask them for the EI booking reference. When they give it to you, you can then call EI to assign seats (if it's long haul). Using the EI booking reference on the EI web site did not work for me, but it's worth trying it once you have it before you call.

If you call, they will ask for the booking reference, your name, and the BA ticket number. This is on the BA booking confirmation e-mail starting with 125-##### etc. So have that ready too Good luck!