I'm in the UK and I've been working in a pensions consultancy as an actuarial analyst for 5 months. This is all the corporate experience I have, as I graduated in 2020 and previous positions are less relevant (maths tutor, coach, etc.). Upon graduating, I wanted to pursue an actuarial career in insurance, but due to the job market and my resume (no internships/relevant experience, only a 1st from a top 50 uni in Mathematics), it was hard to land a good job. I managed to secure a position in pensions, but it has always been my goal to move into insurance, ideally life insurance.
For the last month I have been getting in contact with recruiters and looking and relevant roles on linkedin, and after a few applications I got an interview at a life insurer. The role was advertised on linkedin as £30,000 - £40,000. I am currently earning £28,000 (after I receive my exam results in July this should bump up to £30,000). At the end of the interview I was asked what my salary expectations were for HR reasons, and I said 35k-40k.
Aside from the video interview, all contact with the company has been with someone from HR. He got in contact with me Friday afternoon saying that I have been invited to a second interview as the actuaries felt that I gave a good account of my knowledge and skills as well as my personality. However, he also added in the email that the salary will be "in/around the £30k ballpark", and wanted to clear that up before things were taken further.
The benefits aside from the salary will be similar (study support, pension, etc) to what I currently have. I do not want to change jobs sideways for a miniscule increment, but I do want to get into insurance and start to receive valuable experience as soon as possible. I'm not sure how to best respond to the email saying that I really like the role and company, but I won't move for less than £35k without coming off as rude or harsh.
TL;DR: I want to change roles to a better industry but the pay offered is not what I asked for in the interview.