If you have a job that sometimes involves travel or long high pressure days , is it legal for your boss to not allow you time off to vote?
I would be interested in the situation in the UK and US.
In the United States, I think the best answer here is it depends. As @DA mentioned in the comments, there is no federal law regarding this particular aspect of voting rights. The states (some of them anyway) have stepped up, and I found a pretty useful link here that summarizes the current patchwork of laws.
NB: It looks like that page was made for the 2012 election, so I am taking those summaries to be accurate as of that timeframe.
I think the best summary of the current status of whether or not your boss is required to allow you to "take off" to go vote comes from here:
I'm scheduled to work on Election Day. Do I have a right to take time off from work to vote?
Not necessarily. Depending on where you live, the answer may be "yes, definitely," "no, not really," or "it depends." This is an area of the law dealt with on a state-by-state basis, even during the national presidential elections held every four years. So your right to vote during work time depends on what your state law says.
Looking through the list from the first link, it looks like there's a few broad categories of the types of laws states have (or failed to have) enacted:
1. No specific law requiring time off to vote. (21 total)
Connecticut, D.C., Delaware, Florida, Idaho, Indiana, Louisiana, Maine, Michigan, Mississippi, Montana, New Hampshire, New Jersey, North Carolina, North Dakota*, Oregon, Pennsylvania, Rhode Island, South Carolina, Vermont, Virginia
I am including North Dakota in this list, even though the law "encourages employers to [allow time off of work to vote]" because encourging something is wholly distinct from requiring it.
2. Employees who begin their work day less than X hours after polls open and finish less than X hours before polls close are entitled to Y hours leave to vote (25 total)
Alabama, Alaska, Arizona, California, Colorado, Georgia, Hawaii, Illinois, Iowa, Kansas, Maryland, Missouri, Nebraska, Nevada, New Mexico, New York, Oklahoma, South Dakota, Tennessee, Texas, Utah, Washington, West Virginia, Wisconsin, Wyoming
It should be noted here that each of these states' laws are worded somewhat differently with somewhat different restrictions. For instance, in Tennessee the employee must request leave by noon the day before Election Day.
3. Employees may take X hours off to go vote (2 Total)
In Minnesota, those hours are specified to be in the 'morning'.
This being the United States, there are some notable outliers.
Employers must create schedules so that each employee will have the opportunity to vote.
That's seems fair enough to me.
No employee of a manufacturing, mechanical or mercantile establishment must work during the first two hours after the polls open if the employee applied for a leave of absence during this period.
Apparently the rest of us are out of luck if our employers don't want us to vote.
Employers cannot fire or threaten to fire an employee for taking a reasonable amount of time to vote. Paid only for salaried employees.
And (my personal favorite)...
Election day is a legal holiday in Puerto Rico and most employees have the day off work. Employers running a business in operation on election day, however, must establish shifts allowing employees to go to the polls between 8am and 3pm.
In Regards To Travel
It is my impression that none of the states have laws on the books that take this into account. So while you may be entitled to have the morning off to go to the polls, you may be physically unable to reach your polling station depending on where your employer had you travel to on the day prior to election day. You still have a right to vote, but I would consult your local board of elections and acquire an absentee ballot in order to have your voice heard.
Additionally, many jurisdictions include no-excuse early voting, or in the case of WA, OR and CO, offer all mail-in voting where a ballot is automatically mailed to all eligible voters and there are no traditional polling precincts. The link above provides a color-coded state by state map depicting the current status of each state in regards to absentee and early voting (thanks for the comment from reirab).
Practically, could an employer prevent an employee from voting?
As was noted in the comments, I believe the answer here is yes it is possible. I think from the vast diversity of employers out there and, judging from the fact that many employers urge (coerce?) their employees to vote a certain way certainly implies that the will to affect outcomes of elections is there for employers. However, the possible downsides of doing this to an employee (which include a devout pummeling in the court of public opinion) would no doubt deter all but the most ardent employers from actively preventing employees from voting which, as noted by others, would be minimally effective at best.
That being said and this being the US, we know it has already happened. I stumbled across this series of letters which describe a sawmill owner's efforts to disenfranchize both black and white employees of his from voting for the "radical ticket" in South Carolina, 1868.
Since polling stations are open from 7am to 10pm and it is forbidden to work that long, certainly without a break, it's not clear that any specific rule is needed. If your boss really demands your presence from 7am to 10pm, he or she is probably already doing something illegal.
Furthermore, since you can easily vote by post or by proxy, it could be argued that work obligations do not threaten your voting rights per se. Work is in fact cited on the website as one of the reasons you can use to apply to vote by proxy.
So far as I know, there is no obligation on a UK employer to allow an employee time off to vote.
There is a legal obligation on employers to allow employees time off to perform certain "public duties", notably jury service. See this gov.uk link for more: https://www.gov.uk/time-off-work-public-duties
However voting is not a public duty. Furthermore the legal obligation above does not apply to all employers in all circumstances.
I speak of the law as it currently is. Whether it should be different is a separate question.