Non-refundable hotel advertised free cot/infant bed available but won't provide one.

We just booked a room for two nights at a hotel in London specifically because it said free cots/infant beds available. We included that we will need a cot in the booking notes. We received a reply shortly after booking saying they do not provide cots and enjoy our stay. They had actually gone on and changed the information on the hotels.com app (how we booked it) to say cots not available. I know we booked a room with a cot because as soon as we added that filter we were down to only two options in the location we wanted and at the price point we felt comfortable with. They will not refund us and insist that they never said they provide cots (we actually saved a pdf of the page where they had it advertised) and they're still refusing. This is a fairly affordable room for about a month from now near Kings Cross station in London. They would easily have time to rebook the room, but they're refusing. We need somewhere for our baby to sleep, which they said they provided. It's the only reason we booked this place.

We could barely afford to do this in the first place but decided to prioritize it because my almost 4-year-old asks if every clock tower we see is Big Ben and saw something about a "dream trip" recently and said his dream trip is going to London. We live in Northern England and had a baby recently so we really wanted to do something just for the big brother who has been very patient for months. I hate so much that we're getting messed around by this stupid hotel and the cost could balloon because of it.

So, what are my options here? I can try to get my credit card to block it, but how likely am I to actually receive a charge back on my credit card for this? I believe this would fall under the Consumer Rights Act 2015 if just arrived to not cot and there had not been communication specifically telling us they're not going to do what they advertised, but does that still apply? I am at a loss, like they can't just do this to people, right?