I don't know where you've read that it's recommended to do a half two weeks out (I wouldn't) but given that it's three weeks out from London that does make a difference. Personally the only time I would schedule to run a HM three weeks out is if I wanted to incorporate it into my final long run. So this is an option, but use the HM to practise target marathon pace, adding on a few miles as a warm-up and cool-down to bring it up to 20 miles (or whatever).
On the other hand if you're feeling good, got no injury niggles, you want to take advantage of good form and you've got a HM PB you want to have a go at, running it flat out is also an option. Your call I reckon. Either way, after the race would be a good time to start the taper.