I've also used USA suppliers and these guys have always come through, or Rock Auto. They do both ship US Mail though which does incur Royal Mail handling charges and delays this side (similar to Amayama orders) so never used for cheap or bulky parts. With the USA Toyota dealers, you can only go with generic model parts though as they cannot handle left hand drive specific parts.
On the UK guys, I find Steve is less interested in small value orders than Paul so now push most orders through TCB even if they aren't the cheapest. Another UK option is Burrows Toyota who will give 10% discount (similar to Inchcape Toyota) if you ask. Burrows have an eBay shop which often comes up with useful parts at discounted prices, I just bought a new crash bar from them via eBay for £169 delivered. No one else could match that price which is surprising when you think of the eBay commission on the sale.