Approaching the situation with good data and an open mind is a great approach, and based on what you've shared I think your logic is sound. The salary you have

Approaching the situation with good data and an open mind is a great approach, and based on what you've shared I think your logic is sound. The salary you have now seems to be more reflective of junior product designer (between entry level and mid level). It's worth making sure you have some sound reasoning for why you are a mid-level product designer in case this becomes a point of contention. They should really be looking at this based on your skillset, your output, and what they ask/need of you, but the shortcut (unfortunately) is often looking at years of experience. Just be prepared to talk through why you're a mid-level designer, just in case. I took a quick look at a source I trust for comp information and your range (£58-60k) although pretty tight seems quite accurate. That said, they probably will have their own data. It sounds like you have done your homework, but being able to site a few trustworthy sources is ideal. Last, expect a little push back. Big company bureaucracy means it will likely take them a while to see things your way. They will mention that you'll get more benefits, which are valuable to you and cost them money. They will likely also just take a while. Good luck! Hope this helps.