Yours is a common question. I'm just going to direct you to another current topic on the matter. See reply #3 from WednesdayMarch where she recommends a shop and provides some very sage advice. If you want proper entry-level skates, you're looking at something along the lines of a Jackson Excel, Artiste or Mystique, where the boots and blades come as a package. (there are plenty of other brands too that make good entry level skates, like Graf, Risport, Edea and Riedell.....). You may need to spend more than 100GBP, but think about what a pair of good quality dress boots cost. And you'll wear your skates more, at least in the short term. Check the Facebook market place or maybe even places like Vinted for used. Or even ask around your rink. Admittedly, adult sizes are hard to find.
Another reason to get proper kit, is because the blades will hold an edge better. Sounds like dull blades (which is a common thing with rental skates) are a part of your problem.
I can't get a price on the skates you suggested. They look like something I could get at Decathlon. Will they work? Probably, but I don't know how well or how long the nickel plated blades will hold an edge though. You may end up paying the difference in sharpening fees. People on Amazon complained about sizing, so that's also something to be aware of, and another reason to go to a specialized skate shop.
http://www.skatingforum.co.uk/index.php?topic=7658.msg112892#msg112892