I'm looking at applying elsewhere and I have ambitions to move to one of the larger tech companies. I applied to one of the major startup fin-tech companies in the UK not too long ago, interview process went pretty well, got to stage 5/6 and did very well in technical discussions (discussed messaging systems, transaction integrity with multiple approaches etc), however fell short in the programming task (a program heavily focused on a certain aspect of programming, something I didn't have a massive amount of experience with so got tripped up when trying to convey the intricate details of what exactly the program was doing, though it was completely functional).
Since then, I've improved massively in that part of my skill set, however it has left me with a feeling/fear that I could apply to another company and face the same problem of getting tripped up by a single thing where my knowledge isn't up to scratch, despite my pretty abundant knowledge in other areas. Is this something commonly experienced and if so what can remedy it?
Just keep applying, and realize you may have gotten the job at that one you made stage 5/6 and found out the team was in fact toxic.
Know your worth. They should be excited about you and your unique qualities the entire time and selling you on joining.
If it doesn’t feel that way or you see or hear any red flags, pass on continuing the interview process. Doing this will help build your confidence and save you a lot of time.
Being able to walk away is material to maintaining a high bar for what you expect from people you will be giving portions of your life to.
You as a programmer aren't expected to know everything. If you encounter a company which expects you to know everything in a particular narrow area even though they know you have no prior experience in that exact area, you probably don't want to work with them anyway.
Just go to an interview, do your best and don't worry too much about it. You are either a good fit for them or you aren't... and there are either better candidates than you or there aren't. There's not much you can do about those factors.
I think the interview feedback you mentioned in your comment, not the original post, is further evidence of that about lacking 'deep' knowledge in an aspect of programming - this kind of thing takes time working on real challenges to accumulate, and for people who have spent 5-10-20 years accumulating hard won experience, the bar to consider someone a senior may be a bit higher than 2 years.
Of course this won't preclude you getting a great job, but it might be realistic to set your expectations in line with what others may consider also.
On the other hand, if you inflated your resume and got caught on that (which happens pretty often, I've seen people with a little web building experience try to apply for scientific research positions that require really tough skills, though I'm not implying that was the case here, I just don't know) then stop lying and your success rate is likely to go up.