V class is not available on the flights you want. It is available individually on UA949 and UA 538, but when those segments are "married", H is the lowest class available at this time:

F3 C9 D9 Y9 B9 M5 H5 Q0 V0 W0 S0 T0 K0 L0 G0 P2 A3 Z9 E0 U0

Instead you could catch the earlier LHR-ORD UA923 and connect to UA536. V would be available then (and even W which is fine since these are UA flights and your SWU would work for your upgrade).

UA923/536: F3 C9 D9 Y9 B9 M9 H9 Q9 V9 W9 S7 T0 K0 L0 G0 P1 A2 Z9 E0 U0