Looking at 6/2 eastbound:

34: #003 flat bed
4: #015 flat bed
28: #002 flat bed
18: #113 flat bed
112: #131 flat bed
110: #129 flat bed

Compared to the aircraft for 6/1, you'll find that the IAH-LHR aircraft are dedicated. Which makes sense, as a IAH-LHR roundtrip takes about 19-20 hours.

The EWR-LHR aircraft are rotated with other flat beds in the system.