There are a few younger ATCOs who don't know the difference between
'Leave (fix ABC) heading XYZ'
and
'After (fix ABC) fly heading'.
If instructed to do the former (as you were in your example), then one can and would expect the pilot to manoeuvre the aircraft (within reason) to ensure that the aircraft will fly over the fix on, or as near as, the instructed heading. If this heading is vastly different from the normal holding pattern track, then it will make a difference.
If the instruction is the latter (after fix fly heading), then you fly the normal hold, then turn onto the desired heading.
However, even in the LTMA, we won't worry about the odd mile off track - any more than 3 or 4 in the holding pattern and you may well be quizzed!
As for the comment about accuracy of lateral navigation, radar, unknown aircraft characteristics and unknown effects of wind that was made above, that's not correct in the UK, and certainly not at the levels and speeds you are talking about (i.e. in DAYNE)