It's actually just as quick to take a NX coach from Brum to Heathrow, as it is to take train and then the coach link.
The Green Line 724 takes an hour from Watford Junction to Heathrow, but avoids the M25 so timings are less prone to traffic delays. Or there's the 140 bus from Harrow & Wealdstone to Heathrow which runs 24hrs and also takes just under an hour.