You can claim Local Housing Allowance (as it's now called for new claims) in another area, but you should be aware that the maximum amount payable varies across the country (to reflect differences in commercial rents).
You can find out how much you're entitled to in each area by using the calculator here:
https://lha-direct.voa.gov.uk/search.aspx
If, as your post implies, you're single you should set the 'bedrooms' field to 'shared accommodation' if you're under 35 years old, or to '1 bedroom' if you're 35 or older.
Chris