When you say T1 do you mean all of T1 or just part of it? I'm not familiar enough with LHR as I used to be and I'm curious to know if they are going to knock the entire metal tubing that is T1 and stiffling hot during the summer. The memories of flying back and forth to Ireland in the 90's and early 00's.
The diagrams at the bottom of this newspaper image should explain the sequence:
The old T2 having been demolished, the southern half of the new "LHR-East" / T2A is now under construction. When complete, T1 will be demolished. The northern half of the new terminal will then be built in its place. The existing stands 247-249 and 231-233 (the furthest reaches of the current T1) will become the northern half of satellite terminal 2B parallel to the new "LHR-East" / T2A. I'm not sure whether a further satellite T2C (as shown in the diagram) is certain to be built or not, but LHR surely needs it.
What will remain is a significant improvement: one large terminal ("LHR-East" / T2A) and one or maybe two parallel satellites (T2B and T2C) perpendicular to the runways. The satellite(s) will be connected by an underground tunnel / people mover, allowing for a full sized taxiway between them.
Whether T3 ever gets rebuilt like this is another matter...