AFAIK only Scotland allows wild camping. Personally I would only pitch my tent on camp sites in England. The main advantage of a bivvy is that it is stealthy, so it's easier to "go wild" even where you're not supposed to. The disadvantage, compared to a tent, is that it sucks ass when you have to "make camp" in the rain. If your bivvy of choice is available in multiple sizes, get the bigger one so you have a little room to move around / reorganise stuff with the zipper closed.
If I were to ride LEJoG for speed I would bring a bivvy (+pad +quilt) and sleep between 0:00 an 04:00 or thereabouts. Going for more enjoyment, I would skip the tent and use hostels and possibly b&b's.
FWIW, the
Alpkit Koala saddlebag (regular size, 13L) holds my bivvy, 1/2 length air mattress, thin synthetic quilt, down vest and has a little room to spare. I'd say that if you want to bring a tent your bike needs a rack, and you probably want two small panniers (that sleeping bag will use at least half of one pannier); I can recommend the Ortlieb Frontrollers, sturdy and waterproof. Arkel Dry-Lites weigh about a pound less, but are smaller than advertised and the straps tore off after just 4 weeks of travel...