I've seen a similar question asked elsewhere, and there weren't many specific suggestions. I don't know about the UK in particular, but finding a program like this sounds somewhat unlikely.
I know there are some programs in Australia that have a distance learning component (because I've seen teaching positions in those programs advertised), but I don't know what the requirements or flexibility would be like. There may be similar programs elsewhere, and certainly you could find a way to take a class (or several) but I don't know about completing a program in this way. You would want to reach out to local universities to see what the options are like.
I do believe there are some MA programs in teaching ESL that are primarily distance learning, so that's an option to consider, but I don't know about a degree in linguistics narrowly, or at the undergrad level. There's probably something, but also check on its quality or applicability to what you want to do later-- is this for personal enrichment (in which case you'll have more options) or to eventually continue to grad school and so forth? Your options will be somewhat limited by what you want to do with a degree. If it's "just" a degree, then you may have more flexibility, for example finding
some linguistics courses you can take as part of something else.
I'm sorry I don't have more specific advice on this. The upside is that I think online courses, distance learning, and so forth are becoming more common, so you might be able to find something now, or soon. It also might be a new program not yet widely known, although of course you'll probably be able to find information about it online if you find the right keywords.
Should you wish to ask somewhere else, there is an email list that includes many UK professors who might know something:
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A0=TEACHLINGThat's a list
for teachers, but I don't see why your question wouldn't be on topic given that information is not generally available elsewhere. If they don't know of something (and they might not), then I would
guess there is no program exactly like you're describing. Instead, your best option would be finding a general degree program and hoping to take one or more linguistics class while doing so.
Regardless, there is a lot you can do on your own if you want to read (textbooks or not) or study languages, etc. And you're welcome here at linguistforum!
For online courses you could do on your own (or possibly as part of a degree somewhere, but I don't know the details) there are a few online linguistics courses popping up online these days. The best place to start might be MIT OpenCourseWare, which you can find easily online if you search for it. I believe it's free to read/participate but may require a fee if you want to "complete" the course (get a certificate, possibly transfer credit or something like that).
