United flew from ORD (3x) LAX (2x) IAD (3x) SFO (3x) JFK (3x) EWR (1x) BOS (1x) DEL (1x). That was 17 flights per day. Aslo, I'm sure with the open skies agreement, I'm sure LH or BD (British Midland?) would be more than willing to 'sell' a slot or two to United to increase their value at LHR. Also, didn't UA get all PanAm routes, including beyond London? But I think IIRC UA sold the beyond slots to LH as part of the concessions to obtain EU approval of the code-share.
Corrections?
From the time table 2001 April to June
# Dept-Arr Flight # Dept Arrive Equipment
1 LHR-BOS Flt 999, 1055-1315 767
2 LHR-ORD Flt 939, 0800 1015 777
3 LHR-ORD Flt 929, 1100 1320 777
4 LHR-ORD Flt 959, 1355 1650 747
5 LHR-DEL Flt 002, 1025 2330 747
6 LHR-LAX Flt 933, 0800 1200 777
7 LHR-LAX Flt 935, 1125 1435 777
8 LHR-SFO Flt 975, 0800 1130 767
9 LHR-SFO Flt 966, 0900 1155 777
10 LHR-SFO Flt 931, 1445 1730 747
11 LHR-JFK Flt 957, 0915 1150 767
12 LHR-JFK Flt 905, 1355 1620 777
13 LHR-JFK Flt 979, 1800 2045 767
14 LHR-EWR Flt907, 0950 1225 777
15 LHR-IAD Flt921, 1140 1455 767
16 LHR-IAD Flt001, 1250 1535 747
17 LHR-IAD Flt925, 1640 1930 777
So any way you dice it, I'm sure if UA wants more service to LHR they will have greater ease than about any other US Based carrier with the exception of AA. JMO