A quick wikipedia search reveals the 2001 SC430 has a 3UZ-FE engine, which has VVT-i. "Camshaft variator" sounds like it would be part of the VVT-i system, though none of the literature uses that term. Very crudely summarised, the camshafts will have two profiles and a sensor will cause an actuator to receive increased oil pressure, which shifts the cam.
It seems possible to buy a whole 3UZ-FE for about £1k: https://www.ebay.co.uk/itm/384336285250
The VVT-i is entirely in the heads, so could just buy them instead, for approx £350-ish. Each side of course as it's a V engine, so there's two heads.
(For only £8995 you can add some more horse power )
I'm not too sure about how much it should cost, but it seems like £2.3k is perhaps on the high side. My first suggestion would be to take it so some place like https://www.japex.co.uk/servicing/lexus-service-specialist/ which claims to be good at VVT-i problems for a second opinion. They don't seem to be too far from you, I don't know if you could get it there.