Try Clarkes of Walsham. I bought some very nice real 4"x2" there recently. Invoiced as *paddock fencing rails pressure treated green 4.8m x47mm x100mm* £6.32/length.
+1. Go for brown pressure treated sawn from a 175 mm board. Gives 150mm cover. Don't use creosote. It'll make her eyes smart for weeks. If you intend to finish with Sadolin etc. paint the boards before fitting otherwise you will get stripes when they shrink. Chose which way round to fit the boards and stick to it. Harry says smooth (original board finish) side out; some theory about warping. I use the diagonal cut *out* as it gives a better rain drip and I prefer the rougher finish. The downside is that cobwebs stick like....Tie beams have been covered by others but you might also consider stiffer timber for the door hanging posts and at least 4"x2" for the wall plate.
Ride on mowers are legal tender with our travellers so you might concrete in an anchor for a securing chain.
regards
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