Places like Holiday Autos and Auto Europe are generally best for UK residents. All inclusive rates (no extra insurance to pay) and unlimited mileage.
You biggest problem will be finding something without a hefty one-way drop off fee, assuming that's what you want to do.
And Route 66 doesn't really exist as such - but it is a convenient shorthand for 'the highways that used to be Route 66 and are now something else or disappeared completely and replaced by the Interstate'. I expect you knew that anyway - if not someone's bound to tell you. Still an interesting drive.