Yes, take them back.
I bought a top at River Island 3 weeks ago, lost the receipt but took it back anyway and they gave me a voucher for the price it currently was £15.
I dont know what TopShop is like, but go back and speak to a manager. Most managers dont want customers emilaing customer service, because i would gurantee 90% customer service would have a go at them if you complained them not refunding- as long as you look genuine then they should do it even just out of goodwill.
This is assuming it has a topshop label- if it is one of their concessions you are going to need proof of purchase otherwise you could have bought it anywhere.