My day rate varies ( London more expensive ) but is for 8 hours on site. Have had some clients who think that driving between sites is not included e.g arive at site do 4 hours then drive to next site 1.5 hours drive away, then expect another 4hrs work.
There are other thing to factor parking for London, congestion charge, fuel.
I did a few calls in London for a client the other day total cost of parking was over £60 congestion £10 fuel £12 and supplied parts.
I would expect a bit more to cover for the extra expense than if I had been working on one site for the whole day.
But then again I would have been upfront about this and agreed prior to work.