When a self employed business person travels on business, generally speaking the costs of travel and accommodation will be incurred because of the business and therefore the costs would be allowed against tax. Where, however, the trip is extended to allow the individual to take a holiday at the end of the trip, the whole trip is no longer wholly and exclusive because it is part private, so the costs would be disallowed.
Where the individual travelled by first class train or air, while it might be possible to argue that the business did not require them to travel first, and that economy would have been acceptable, this is not a point that is often raised by HMRC. In reality, the first class train journey may allow the business person to work en route, or to arrive more rested and ready to do business, so there is usually a plausible business reason for incurring the expenditure, and any personal benefit such as increased comfort is normally disregarded. If the expenditure was excessive, such as chartering a private jet, then this might well be challenged.
The same is true of accommodation costs and meals taken when away on business. There is no requirement to go for the cheapest option, but reasonable costs will normally be tax deductible.
In the case of income and corporation tax, there is a specific ban on tax relief for entertaining expenditure, so any restaurant bills which relate to meals taken with customers / suppliers / contacts would be disallowed, including the element that relates to the proprietor or employee – claiming that they would have been able to charge had they eaten alone isn’t sufficient as this again breaches the “wholly and exclusively” rule. Note that the rule about whether this would be taxable on the employee is quite distinct, and it is rare for an employee to be taxed on the benefit of entertaining clients.