Your contract is with the shop, not somebody else that they sent it off to
how old is the pram ? Under 6 months and you can ask them to prove that it didn’t have a fault when purchased. After 6 month you may have to show that it did have a fault (of course that may be obvious from what you’re saying)
(that’s sale of goods act, not warranty. warranty may add to that cover but it can’t reduce it)
it’s come back just as broken as when it left
Under sale of goods, they should refund, replace or repair (your choice, I think). If they can’t repair there’s only 2 options left
Disclaimer: I am not TJ
try this – probably still correct