If it was already noted as damaged, I would expect LL to replace it. We replaced ours when we were in rented because the inventory clerk failed to notice that it wasn't actually fixed to the loo (just balanced there) and we couldn't cope wobbling about on it.
It's the kind of thing that I would buy and install as a goodwill gesture to my LL. Think not quibbling about the small stuff helps maintain a good relationship and makes a difference when the Big Things go wrong. Not sure I'd spend £40 on a bog seat though, are you sure you can't put a cheaper one on? IKEA do decent ones for about £15.
It's a funny shape at the back with unusual fittings, so I think it needs to be the exact model.... I am going to scour homebase today, see if they have something cheaper that might fit, but I am not holding out much hope.
We have bought about 6 toilet seats over the years (in our numerous rented houses). Not because we have unfeasibly large arses and keep breaking them but because they have always been really skanky. We're moving again shortly so fully expect to purchase loo seat number 7 soon! We just accept that it's one of those costs that we bear and wouldn't ask the landlord to pay.
A padded toilet seat???? I thought our duck egg blue was edgy!!
You can get an amazing value one at Wilkinsons, if there is one near you. It is white lacquered MDF moulded wood and comes with metal hinges which appear to be chromed brass. It costs £10 and is very solid. Most cheap seats are lightweight flimsy plastic.
Keep the receipt just in case it goes wrong and they will exchange it for you.
I fitted one and found it helpful to fit black rubber tap washers between the fixing nuts underneath, and the porcelain. This grips well and prevents it moving. Cheaper seats usually have plastic hinges with plastic bolts and nuts which are not very strong. The packet of tap washers might have cost me 50p or something. You need a pozidrive screwdriver to adjust the hinges on your WC pan (you can adjust for hole spacing, also adjust the seat backwards and forwards.