Getting my Deposit Back

So, before I received my results, I booked for the Exeter One Private accommodation. When I first booked it, it was under the company "wearehomeforstudents." I paid a £150 deposit to secure my room then waited for my results back.
About a month later, the company in charge of the property shifted to "Mansionstudents" and I had to re-sign my tenancy agreement. After I received my results, I found out that I did not get into my Uni of choice in Exeter. As a result, I had to call up Exeter One to ask if I could transfer my lease to someone else. I did this, and I was told I would receive a portion of my deposit back.
Once the expected time frame of receiving my deposit back passed, I called "Mansionstudents" to ask where my deposit was, and they said, when I resigned with them, my deposit should have been paid back to me from the original company. I then contacted "Wearehomeforstudents" and they said that the deposit was being held by the new company. "Wearehomeforstudents" has the deposit secured under TDS which has listed me paying £150 yet they continue to insist the new company has it, even though I checked the agreement for "Mansionstudents" and they not only use a different service to secure my deposit, but in the contract, it also listed that my deposit was £0.
I contacted TDS, and they had stated that the only way to get my deposit back is to provide my deposit account number, which isn't in either of the tenancy agreement documents, or the confirmation email I received from TDS. Is there anything that I can do in this case because it's now been 2 months since my lease has been officially transferred and I still haven't received my money.
I have proof of purchase, the email exchange between me and the new tenant, the confirmation email from TDS, both of the leases, and months of emails of me being bounced between these 2 companies.