Selected banks and building societies -- in the UK -- have been giving an introductory rate (sometimes referred to as a bonus rate) to customers who open a new easy access savings account. The introductory rate usually lasts for 12 months, then the account transfers back to the standard rate. At present, July 2018, most standard easy access savings accounts pay a low rate of interest to existing customers: in the region of 0.1%-0.5% interest. With CPI inflation currently running at 2.4%, its wise to look for new accounts that bring savers closer to that rate of interest.
As it's free to open a new bank account, there is nothing stopping consumers continually opening a new account every year to take advantage of a bonus rate. There is certainly a valid reason to keep opening a new savings account every year: if savers do not do that, then they will typically receive 3x less interest. The drawback is the effort required to open a new bank account: such as sending a photo ID through the post. However, switching a savings account typically involves less work than switching a current account: as you will need to use a CASS transfer (take seven working days) to switch all your payments from one current account provider to another. While it is simpler than it was to switch a current account, it can be prove time consuming if an overdraft balance has to be switched. Therefore, while it takes a little effort to open a savings account, it is still far easier than with a current account.
Not all banks offer an introductory rate, they typically seem to be offered by the smaller high street banks, or by banks who do not have a high street presence. Accounts with an introductory bonus often need to be administrated online, by post or telephone. The Post Office and theAA are two examples of companies -- not generally thought of as financial institutions -- who have regularly enticed savers with a 12 month introductory bonus. Unlike with some other banks, the Post Office have attempted to keep savers by providing a reasonable good savings rate after the 12 months ends: the accounts were named "Online Reserve". Birmingham Midshires, owned by Lloyds Banking Group, are another company who regularly offer an introductory bonus for Internet savers; Birmingham Midshires is an amalgamation of fifty building societies that included the Midshires and Birmingham building societies. At present (July 2018) the following banks and building societies offer an introductory bonus rate: Birmingham Midshires, Bank of Cyprus UK, Coventry BS, Post Office, and Tesco Bank.
While current accounts will rarely have a large introductory bonus rate, they do sometimes offer perks for new customers: cashback or rewards for depositing a set amount of funds per month etc.