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Wickes normally have very competitive prices for wood, if you can be bothered. I think Barking would be your nearest.
Otherwise, your local builder's merchant. I have bought many 4 x 4s, 2 x 2s and many many other things from C&S in Leyton which must be near you. Maybe very slightly more than Wickes but the quality of their stuff tends to be better too. If you do go there and get served by Jit tell him I sent you.
I got mine from somewhere else in the end, simplygardenbuildings/A1 sheds which was already a lot more than 5% cheaper than Shed Store for the one I wanted.
Any recommendation for where to buy pressure treated 4 x 4s?