Sorry but I am afraid that you will have to despair. People often think that employment law offers so much more than it does, and in the end the only arbiter of whether something is lefgally fair or not is an employment tribunal. Good practice may dictate a formal process, although often that formal process is not much more than a written version of what I just told you. But no - HR do not have to be involved. There is no legal requirement.
Your current position is that you are at risk of redundancy because your role no longer exists (the fact that it exists in another country is irrelevant - it no longer exists in the UK so the post is going/gone). If there are up to 19 people at risk (and I assume not) there are literally no legal definitions of what consultation looks like. Nothing at all. They can literally have it done and dusted in a day.
If it is 20 or more there are some rules they have to follow, and some minimum timescales, but no matter what anyone tells you about "meaningful consultation" it is incredibly easy to make it far less than meaningful and get away with it.
The only test in law that might apply to you is that they need to offer you any possible alternative employment that might be available to avoid unfair dismissal - if you get to the magic 2 years service. But be very clear - what you think is a suitable alternative and what the law thinks will, I guarantee you, be very different things. So your comment that you view a possible role as a demotion - well no that isn't relevant, especially since it is possible for an employer to argue, in the right circumstances, that an ACTUAL demotion is a reasonable alternative. And if you choose to refuse a suitable alternative you may be kissing any redundancy pay farewell - legally they can not pay it if you refuse a suitable alternative. Again, the arbiter of what is suitable can only ever be a tribunal - and they are often a lot harsher about what it means than you would think. Less pay - possibly suitable. Lesser terms - also posssibly suitable. Don't like the role - do not even think they will side with you on that one!
Sorry, but if this is just you, then they can make it a very uphill struggle, and what you want and what you may get aren't likley to be remotely similar. If you see a job that suits you elsewhere, go for it. I can promise you that that is the best and only way to really protect yourself.