How do I figure out if I'm being underpaid vs market average for my skillset?

I originally posted this in UkPersonalFinance but it was removed for not being on topic.

I work as a client delivery analyst, for one of the big 3 credit reference agencies.

Over the past 18 months, theres been a lot of discussion between colleagues that our analysts are underpaid compared to similar positions elsewhere. Whenever someone has left theres been rumours of them getting big pay bumps where they're going.

I hadn't put much thought into it because I'm fairly happy with my pay, but historically I've had very low expenses (no kids or pets, below market rate rent and splitting everything with my partner). I'm about to move and expecting a large increase in expenses, nothing that will mean I'm struggling with money but it got me thinking. I want to be in a good position to start a family soon, and what with the cost of living crisis my expenses are only going to keep increasing.

My partner suggested I have a look around to see what I could be paid elsewhere, so I can take a proposal to my manager, but the percentage of job adverts that have a salary on is incredibly low.

How can I figure out how much my skills are worth?

I'm based in the midlands, currently paid around £35k. This is a summary of my responsibilities and skills:

- I maintain bespoke software solutions for clients, making, testing and deploying requested changes. Pieces of work range from a few days in complexity to projects taking several weeks. - I liaise directly with 2 clients, managing their individual pipelines and summarising into a team pipeline where I either delegate to junior analysts and liaise with other analysts on or above my level to assign work (where I'm not taking on the work myself). - I provide analytics to the clients on product performance and advise on solution optimisation to improve product performance - I manage one analyst who I'm currently still training up - I am proficient in SQL & Excel and have an integrated Masters in Mathematics (MMath 2:1) graduated in 2015