Is travelling from home directly to a different workplace (not my usual workplace) classed as business travel?
Yes, if there is no requirement to report to your usual workplace before business travel and it is not cost or time efficient to do so, then travelling from home to a different workplace is the most practical solution. Your usual workplace is defined as the workplace stated in your contract of employment.
If travelling by car section 3.21 still applies; 'mileage allowances are paid for the actual distance necessarily travelled, excluding the cost of home to work journeys'. In other words a deduction of your commute to your usual workplace will be deducted from business travel if you are claiming mileage allowance.