WI. Harold does not come south

After winning the Battle of Stamford Bridge, Harold legged it south and lost at Hastings just 3 week later. But WI he waits for the Bastard maybe a little north, or south of London. How could this play out?
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William will burn the countryside and force Harold to attack him. However, Harold might have more troops and in better shape (not sure if with higher morale) and might win and give the Bastard the promissed 6 feets of English soil....
Not rushing can only strengthen the Saxon cause. William can't wait in the south forever as his supplies are dependent on good seas and winds. He would have to go forth and seek battle while leaving garrisons along his line of advance further weakening his army. All this while Harold rests and calls in more reinforcements.

Saxon moral would remain high even if Willians force sacked the countryside, they had just won a crushing victory against the old enemy.