While day-counting alone may not disprove UK tax residence, it is certainly important for anyone who wants to be considered non-resident for tax purposes.
It used to be the case that when travelling internationally, both the day of arrival in the UK and the day of departure from the UK could be argued as not counting as days of UK presence. However, since 2008 it has generally been the case that you should include all of the days in which you have been in the UK at the end of the day (i.e. at midnight).
There is an exemption for international transit: if you are a passenger travelling between two foreign countries via the UK, and you arrive in the UK on one day and leave for your next non-UK destination on the following day, you will not have to count the day of arrival as a day of presence even though you were still in the UK at midnight at the end of that day. Neither will you count have the day you leave the UK. Unfortunately this exemption only applies if while in the UK you do not engage in any activities that are not substantially related to completing travel to a foreign destination – i.e. you must count as a day of presence in the UK any day where you are in the UK at the end of the day (midnight) and have you attended a business meeting, visited a property you own, arranged to meet people socially or attended social activities.