After a certain period of time, a criminal conviction for drink driving will become 'spent' under The Rehabilitation of Offenders Act 1974. Once 'spent', you do not usually have to declare the conviction, and can answer 'no' when asked if you have any criminal convictions, although certain exceptions apply. The rehabilitation period will depend on the exact sentence you received. More information and rehabilitation periods can be found here.
Your conviction will become 'spent' after a certain period of time (the rehabiliation period) depending upon the exact sentence you receive. For a fine, probation or community service this is 5 years. For a driving ban, the rehabilitation period is the length of the ban. However, if you receive a driving ban and a fine then the longer rehabilitation period applies which would be 5 years.
For a list of rehabilitation periods, when a conviction is classed as 'spent' and information about declaring your criminal convictions please see here.