The reason Fast Track immigration exists at T3 is essentially that's historically where all the intercontinental passengers arrived. Before the mid-eighties when T4 opened, T1 was for domestic flights, T2 for European flights and T3 for intercontinental flights. There were exceptions even then (mostly that European flights on BA actually used T1, not T2), but with most non-Europeans coming into T3, having an immigration fast track there made sense.

Until the opening of T5 and the realignment by alliance that is following it, most airlines hadn't moved, so most intercontinental passengers (who weren't arriving by BA) were still arriving at T3.

Now, of course, United have moved to T1, where historically the number of non-European passengers has been limited. As such, up to now the terminal hasn't needed an immigration Fast Track to the extent that T3 has. Maybe it needs one now, and certainly with the realignment the old assumptions about the mix of European/non-European passengers in each terminal are changing.

Presumably BAA have either looked at this and decided there still aren't enough non-Europeans coming into T1 to justify a Fast Track, or they have decided there are but there isn't the space/money to build one, or they're planning one for the future. I don't honestly know what the current thinking is.