As they are a business seller, they should be aware of your consumer rights which say you are entitled to a repair, refund or replacement within the first 6 months after purchase. You don't have to prove they are faulty and any new footwear should last more than 2 or 3 months, especially footwear as sturdy as wellington boots.
The address of the seller is on their listings. I would write a letter to them, informing (reminding) them of your rights and asking for a refund or replacement.
If they then want the boots back so they can return them to the manufacturer, that is up to them. But, they sold you the boots and they do have an obligation to sort this out.
Write to them or ring them.
"There are two ways to be fooled. One is to believe what isn't true; the other is to refuse to believe what is true.”
Søren Kierkegaard, Danish philosopher (1813 - 1855)