How far were the British trenches from the German trenches at the battle of the Somme?

Typically less than 1,000 years between the front line trenches, but in some places the distance was as little as 100 yards and in other places it was longer.

There were additional German trenches behind the front trenches, typically spaced between 2,000 and 3,000 yards apart for the main defensive trenches (as opposed to communication trenches). I believe the Germans had 3 lines of main defensive trenches in the Somme sector, and beyond that were rear areas holding brigade and division command posts, artillery parks, supply dumps, hospitals, maintenance areas, field kitchens, and the like. This area was more sparsely populated, and would have stretched for perhaps several kilometers. Beyond that, the countryside wasn't too different, except for German occupational patrols, transportation networks, and larger supply dumps for the routing of supplies to the forward dumps.

Also note that the French fought on the Somme as well. They weren't in as great of numbers (much of their army was either holding the line in quieter sectors or fighting viciously at Verdun, and their entire army rotated between sectors so that no one got a "soft" assignment while other men suffered at Verdun for months on end), but they did contribute significantly, with 3 corps assigned to the initial Somme offensive (compared to 6 British corps).

Six hundred forty-three feet, seven and a half inches.