As a University Researcher, you should have access to some 'free at point of use' network storage. A small amount of network data space is on the School servers, which appears as your home space ( in linux) or your M: drive(in Windows). You should also have access to your allocation on the University's Research DataStore, which is currently 500GB/researcher.
If this is not going to be enough for your research purposes, you can increase the amount of network filespace provided to you on the Research DataStore. This will cost real money but, as long as you have the money, it can be extended to provide what you need.
Currently the cost of extending your DataStore allocation is £200/TB/year.
If you're about to apply for a grant to allow you to engage in some cutting edge science which requires you to store and/or process huge volumes of data then you should include this cost in your proposal , so that the cost of extending your DataStore allocation is covered and you will have access to a secure , backed up network storage for your research data.