Companies won’t always tell you the salary pre final interview, and as a rule of thumb, you shouldn’t bring it up before then.
Prove/evidence your worth and capability and then have the discussion.
There's a difference between an absolute salary offer and an indication of what the salary is likely to be. It's a waste of everyone's time if you go through a multi-stage interview process and then at the end they can't make you an acceptable offer. You don't need to know what the offer will be (which as you intimated would be influenced by your worth and capability that they determine during the process), but you need to know the ballpark so you can dismiss it early on if you are poles apart.
Plus, there’s more to a job than just money. Not all companies are looking for people only driven by money, so if it’s one of the first questions you lead with, it might be an indicator that you’re not the right person
Not saying don’t bring it up, just saying that you should try and judge the situation and make the best of it according to your needs.
I do agree with this however - you need to approach it the right way, making it clear that that it's simply ensuring that hygiene factors are met to avoid wasting their time. It's much easier to have these conversations with a recruiter, I wouldn't raise it directly with the interview panel as you want their impression to be of someone that is keen to help their organisation and progress your career there, rather than just someone looking for the biggest paycheque.
I always seek clarification on the package from whomever I'm dealing with on the hiring front (external/internal recruiter), I tend to find this an easier conversation if they've made the first approach (rather than me submitting an application) as I can then cite it as a knockout question "to avoid wasting your time". Doing it in written form is also sometimes easier because it gives you thinking time to craft your responses, compared to a verbal conversation where an experienced negotiator might back you into a corner where you feel pressured to disclose more than you want to about current salary.
I asked what the salary was. I got told there is no set figure/range and it depends on current salary
This is concerning as your current salary should not be relevant to what salary they will offer for the role, all that matters is your aptitude for the role cross-referenced with your salary expectations. If you got a 10% payrise tomorrow that doesn't instantly make you 10% better at another job. Conversely if you are a CEO who chooses to take no / nominal salary, that doesn't make you worthless.
Some people are underpaid (I used to be one of them). That doesn't make them bad at their job or lacking experience and using current salary as a factor in future salary just perpetuates the problem. If an underpaid person moves to a new role with anotherlow-ball salary then it won't be long before they feel undervalued again.
You said in the OP that you’re wanting a salary at least £40k above where you are now.
Are you that underpaid currently or is the role a significant step up? Just trying to see this from the company’s POV.
The issue here is if the company is using current salary as a proxy for skill/experience. It's highly misleading in some cases (in both directions, you sometimes get people who are paid more they should be based on their skill, what they are delivering etc). So if they are going to say "ah, this person is only earning £x, so clearly they can't have much responsibility atm and don't warrant a decent wage" rather than actually probing that subject during interview, it jeopardises the process somewhat. Anecdotally, if I look at the job I had with most responsibility and where (IMO) I added the most value, it paid less than the 3 jobs I've had since with lower responsibility. I would have been more than capable of doing my current role back then when salary was £40k less, it's not like I've massively improved since. From the other side of the fence, I once interviewed an internal candidate who'd not worked in the discipline directly and was on a relatively low salary in another area of the business (significantly under market rate for the role we were hiring). However, during interview it became clear that she had quite a few transferrable skills, and was already doing some elements of the role. If I just looked at her prior salary and said "nah, she's clearly too junior" that would have been a lose-lose situation for everyone.