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Enforcement by firing a person could be a problem. There are specific allowed reasons to fairly fire an employee, which does not include "failure to vote". The description of unfair reasons includes, as an example, joining a trade union, and other actions that have some imaginable connection to the workplace. But the government has not clearly declared that political expression (or its lack) is or is not fair grounds for dismissal. Such a firing would be subject to scrutiny under the unfair dismissal doctrine, which means that the two sides would seek supporting analogs in UK case law.

The factors that favor a "fairness" finding are heavily weighted towards the legitimate business interests of an employer. This article analyzes free speech rights in connection with the unfair dismissal doctrine. As an example, in Smith v. Trafford Housing Trust, the claimant was punished (demoted) -- unfairly, the Employment Tribunal found -- for expressing a political viewpoint on Facebook. The Tribunal noted that the outcome would have been different if claimant had promulgated his views in the workplace. If an employee's action brings a business into disrepute, perhaps a dismissal could be found to be fair. But failure or refusal to vote does not have that effect: it is not a legitimate business interest of the company whether the employee votes.

If you're an employer who really wants their employees to vote, there are much easier ways. Arranging a minibus to the voting booth and the rest of the afternoon off for those that go to the voting booth would be the most obvious solution. Compared to the cost of lawyering up and trying to put together a legally-enforcable contract, plus the cost of enforcing it, a couple of hours off for your workers is likely to be a whole lot less expensive. There's no need to use a stick when carrots are cheaper.

And yes, as an employer you would be entirely within your rights to tell employees who didn't go to vote that they wouldn't get the afternoon off. Employers can give discretionary time off however they choose.

Good answer already from user6726, but an additional consideration why the original contract could be ruled unlawful would be if an employee's belief in a right not to vote could be considered a "philosophical belief" under the Equality Act 2010. According to ACAS, criteria for this had been defined at an earlier (2009) tribunal.

The ACAS link compares religions with other philosophies, but there are also religions who advocate political disengagement. If an employee was politically disengaged for religious reasons, it would be easy to argue that the contract constituted discrimination that was prohibited by the Equality Act.

Assuming the question is targeted at any part of the UK: in Northern Ireland it is specifically illegal for employers to discriminate against people based on their political opinion:

(1) In this Order “discrimination” means—

(a)discrimination on the ground of religious belief or political opinion; or

(b)discrimination by way of victimisation;

(I believe in the rest of the UK this isn't explicitly protected, however - as pointed out in the comments - "religion or belief" is now interpreted to include political opinion.)

You could probably argue that choosing not to vote is a political opinion, and therefore forcing people to vote would be illegal in NI.

No. You are not allowed to discriminate (in most Euro and Anglo countries) based on religion, political position, or national origin.

Someone's religion might prevent them from voting, e.g. Due to a clerical order because of some issue at stake, say.

Off the top of my head, Sinn Fein refuses to participate in anything that legitimizes Crown control of Northern Ireland. There could be other cases.

Someone might have the right to work in your country, but not citizenship and hence would be prohibited from voting. Say, if your worker was from the EU but not your own country.

You can't say "You *must vote" without implying there is an "Or Else". Whatever the "Or Else" is, it's discrimination.

So firing them for not voting becomes a pretense for firing them because they're Pastafarian, non-Ulster, or foreign.