BBC HD should be ok.
ITV HD may be a problem. It is broadcast as a data stream with the H.264 video inside an H.222 stream. Most boxes cannot detect it because it is a data stream rather than video.
the full parameters are:
28.5E
11428 H
2/3 FEC
3401 VPID
3402 APID AC3
2326 PCR PID
266 PMT PID
54207 SERVICE PID
10510 STREAM ID
0 TELETEXT PID
Video Type H.264
I dont have any hd equipment so cannot check, maybe others can