Speaking from personal experience - the undertaker (in top hat and all the trimmings) will walk in front of the cortege for the first few hundred yards only, then gets in the hearse, and the cortege continues at normal driving speed for the rest of the journey. At least, that's exactly what he did at my mother's funeral, it was five miles from the house to the crematorium, he certainly wasn't going to walk all that way! So usually the hold-up will be minimal. Wait! It's someone's life completed, it's an important moment.
Incidentally we gave directions to all those who attended the funeral, including those who started from my Mother's house in their own cars. Most of them knew where the crematorium was, anyway.