Once a point is reached where one no longer needs immediate access to savings and can begin to save long term for the future, the standard procedure is to establish a 3 or 5 year 'ladder'. One higher interest 3 year fixed term account is opened yearly, and the process is repeated in the following years. Then, in each year, 1 of the 3 accounts will mature and the proceeds are re-invested in another 3 year account. Rinse, repeat.
Unfortunately, currently the rates for 3 or 5 year fixed accounts are only slightly better than those available for 1 year accounts. If rates do rise, then having the funds tied up in a 3 year account at lower rates becomes a losing proposition.