I know it's frowned upon, but if you end up in a personal relationship with someone at the office, what's the most professional way to go forward?
Should you declare it with your managers? What amount of displays of affection are appropriate?
Let's get this out there straight away: no displays of affection are "appropriate". In the office you're colleagues and not lovers; you're not going to win any friends at all by conspicuous displays of affection.
Assuming your contract doesn't explicitly prohibit dating a colleague then act like normal colleagues in the office and do whatever you want outside the office. If either of you have any level of responsibility for the other (managerial/project-based etc) then you need to tell your manager and request that one of you be moved away from the other to avoid conflicts of interest.
If your contract does explicitly prohibit dating a colleague and neither of you have any level of responsibility for the other I'd be surprised (IANAL) if that clause is enforceable in the UK.
tl;dr In the office you are colleagues and there is the potential for conflicts of interest with and within the business. Ensure that there is no conflict of interest then do what you want and be aware of the potential consequences of the relationship not working.
I've seen this a few times, as well as been in these relationships myself. Including dating a colleague that I was technically responsible for, since while I was not her manager, her manager was reporting to me at the time. It was heavily frowned upon and resulted in being the sole reason for me being disregarded for a promotion. So if possible, I would highly recommend keeping your relationship strictly out of the office and making sure management don't find out about it. That, of course, has it's own drawbacks and will not hold forever (especially if either of you use social media or have friends inside your place of work).
In my contract it did specifically state that personal relationships with colleagues was prohibited to prevent a conflict of interest. While this was brought up when I informed management of my relationship, no punishment was enforced (until of course, they let me know it had dropped me out of the running for a higher position some months later). So from that I would take a safe guess that it's not legally enforceable in the UK, otherwise they would of done something worse (they were not the light-handed type of company). But if in doubt or if you become threatened, seek real legal advice.
If you can get away with it, I would suggest showing absolutely zero affection inside the office (strict zero, absolutely not a slight sliver of affection in any way beyond how you would treat anyone else). Then should management come to learn about it, you at least have the recourse that you didn't think to bring it up simply because it does not affect your work or how you behave around any of your colleagues, including your boyfriend/girlfriend. If you show that you can keep your relationship purely outside of the building, they are likely to be uninterested.
Also of note, this also means no emails beyond work related subjects... working in IT has taught me that if a company suspects unprofessional behaviour, they tend to check your work email before talking to you about it (and browser history, so going onto hotmail won't work either, as they'll just jump to assumptions). "It doesn't affect my work" falls flat on its face if you're manager thinks/knows you've been emailing.
I'm not going to give you any relationship advice, but here's my experience: Work place relationships are hard work. The relationship I mentioned before fell apart after she got a disciplinary for not meeting deadlines, and I refused to "pull strings" to get her out of trouble. If you ever have to choose between professionalism or the relationship, you've just hit a pure lose:lose situation, one that could cost you your job, relationship or both. So please be careful, and good luck to you both!
At some point you'll have to decide how serious the relationship is. It is possible that one of you will have to choose between the job and the relationship. If neither of you want to switch to a different job, that can be a very hard choice to make.
Should the two of you break up after one of you has quit the job, there will likely be hard feelings. And that situation is not easily resolved.
If you decide the relationship is serious enough that you will go on with it despite the risks, then you may have to take steps to resolve the job situation.
Before you consider leaving the job, you should consult the company policy. Some companies don't mind co-workers being in a relationship. If nothing is mentioned in the company policy, I would expect the company to be fine with it as long as neither of you is superior to the other and you don't get so distracted by each other's presence, that you aren't doing your job anymore.
If a relationship is not acceptable as long as you both stay in your current position, one of you might need to look for a new position. The new position could be an internal transfer to a different position within the company or a job in a different company. If you already now foresee that one of you may have to leave the company, then you may as well start looking for a different position.
Remember that the line between friendship and a relationship is quite blurry. As long as you are not sure which side of that line you are on there is no need to hand in your resignation just yet. When looking for a new job it is usually in your own interest to only hand in your resignation after the new employment contract has been signed.
Should the company upon receiving the resignation offer to make an exception to the policy in an attempt to keep you, then I would recommend getting in writing that the company cannot fire either of you or impose other sanctions due to your relationship.
Should you be able to both keep working in the same job while being in a relationship (which I hope will be the outcome), then your question about what amount of displays of affection are appropriate will be relevant.
As a guiding point I suggest you pay attention when your co-workers' partners are visiting your workplace. Don't exceed the level you see in those cases. Additionally when business partners or customers are visiting your workplace, I would refrain from any display of affection which you wouldn't do to the rest of your co-workers.
First off, I would consult your employee manual. Some companies outright prohibit romantic relationships with office mates. If a prohibition exists in policy, it can range from outright prohibition regardless of title to prohibition of employees with seniority having direct romantic relationships with subordinate employees.
Your wisest choice is to avoid it. Romantic relations in the office can really impact other people for the worse, especially when such relationships don't work. Office romance is wrought with issues that will inevitably effect people, not just the work everyone is tasked with.
With that being said, if you choose to pursue such, it would be wise to consult your manager. Ask in general terms if there is a policy against employees dating coworkers. If your manager expresses there is written policy against such, then you have your answer. At that point you either choose to be in violation of policy and cease, or you continue and look for another job potentially. Otherwise if there isn't a written policy, you proceed with caution, but expect your work, performance and conduct to be scrutinized more than others in your job.