How much does a carpet fitting cost?

So I have a quite small one bedroom flat, the living room is average, the bedroom is on the smaller side as there would be no room to really walk if I got a king sized bed and I can't fit too much in there, there's a narrow hall where all the doors for the rooms are and there's a little storage room. so it's 2 rooms and a bit in the hall and the little storage room at the end. I can put pictures if necessary. I was in rough situation so this was my first place and I didn't have anything at all so I was getting support and was offered a free carpet as it had been donated, I believe the carpet place donated it to the organisation that helped me and the offer was a free carpet with underlay and just to pay for the fitting. (I add this context to explain how I've been offered a free carpet, it wasn't a scammy deal from the carpet shop or anything like that, it's genuinely been given for free to help me) They took some time to contact me and finally they've measured the place last week, I was recommended by who measured it to get a welcome mat fitted as a carpet might make it difficult to open the door. I've just been told it's going to cost £310 for the fitting. I'm assuming some of that is to pay for the welcome mat too as that wasn't donated. This seems like a lot of money for just a fitting for a small flat. Is this really how much it costs? I'm in the NW of England, is this the norm for carpet fittings? Is it that they're making up for the price of the "free"carpet? It just sounds like a lot and going on Reddit and Google it seems it's about £20-35 an hour or 70 a room, with my situation it doesn't seem like it should cost that much, unless getting a welcome mat is unusually expensive? I'd like some guidance here as I just don't know enough about this stuff