To ask what to do?

[Nochecita]

My flatmate damaged an expensive item of (landlord's) outdoor furniture by burning it accidentally. He immediately offered to sort it out "after payday". Three months later and nothing. I gently reminded him earlier and just got excuses. Why say you'll do it if you won't?!?!

Relax, seriously. Why bother getting it fixed now? It's almost winter.
Why does it bother you so much?
Dobbing your flat mate in to the landlord? Are you 12?

Tell your landlord and let him deal with it.

Easy.

No replacement. You need to inform the landlord and explain the circumstances.
Don't be shy and don't try to pretend it didn't happen or that you don't know who did it. Your flatmate needs to owe up.
The landlord needs to assess the damage and can organise repairs with a supplier of their choice.

It's not dobbing him into the landlord. It's the landlord's house. Most rental contracts state that you have to report damage.

Dobbing your flat mate in to the landlord? Are you 12?

Or maybe she doesn't want to have to pay for a costly repair that had nothing to do with her. The LL may not care who he gets the money off and would most likely take it from everyone's deposits.

A friend once flat shared. Paid his rent and half the bill money to his flat mate and even got receipts. The flat mate pocketed it all. 6 months later they got kicked out and the council and utilities chased them down for the never paid bills. As my friend was easier to locate and had a job, they chased him. Not one organisation had any interest in trying to get money out of the one who actually stole the cash and my friend had to pay his share again plus the housemate's share (except rent. The LL was accepted just his share of rent again off him!)

No way would I leave myself open to be liable for someone else's costs.

Depending on the amount of damage, the landlord might be ok with you just painting the decking. Assuming it's just cosmetic and no giant holes in it etc.

Worth checking with them.