Unlike general elections (where there are procedures already laid down by existing legislation), each referendum in the UK requires an Act of Parliament to passed in order for it to have effect.
The Cabinet Office Code of Practice specifies a minimum consultation period of twelve weeks before a bill can be drafted but the actual period can be much longer. Once a bill has been drafted it's formally presented to Parliament in a first reading, without any debate. Then roughly a fortnight has to pass before the second reading can take place. A bill would then normally pass to committee stage and hence to the report stage before going on to the third reading. The bill then has to go to House of Lords, who might seek to quash or amend it (potentially delaying its passage, with the bill passing backwards and forwards between the two Houses many times) before finally being approved in the House of Commons and given Royal Assent.
Once all that's out of the way, there would then be practical issues to be dealt with, such as getting the ballot slips printed, arranging for the use of suitable venues as ballot stations, recruiting election staff, etc.
So it's hard to see how the whole lot could be achieved in much under a year.