maybe have a look in the rear arches and see if theres been any rubbing on the shock absorbers

My Cooper S made the exact same sound even on the straights, it turned out to be a worn hub bearing

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im with cookies dad, sounds to me like a shocker squeak, and if hes cornering fast on bumps it will go squeek squeek squeek

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-jamie-
1963morris 850
1965 solid side van
1994 rover racecar

Mine made squeaky noises on corners or uneven road surfaces.
Turned out it was the LH rear companion box `oil canning' ie. doing a `woop-woop' Rolf Harris wobble board impersonation.
A block of wood and juducious use of a BFH fixed it.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

It seems fine when driving straight at any speed, I drove on the expressway and it pulled 120 nicely anyway thats beside the point. Yeah it could be the shockers...I used to have similar sounds even when driving straight and i thought it was a bent speedo or something, turns out it was the shockers and my dad made new bushes for them...so that could be the same problem when turning

Im pretty sure i know what the problem is, The drum brakes are scratching against the backplate.....Ill look into it on the weekend, it will be fairly easy to fix as i will be able to see metal scratch marks where its rubbing against (if that is the problem)