To put a little fact on all the judgmental opinions expressed above, the law as I understand it is this.
If convicted, you are legally obliged to declare the conviction to a potential employer if so requested to do so. Failiure, as mentioned above is falsifying evidence and would lead to summary dismissal.
Your conviction will be granted a period before it is known to be 'spent'. After this period you are legally entitled under the rehabilitation of offenders act 1974 to withhold information about the conviction as it is deemed to have become 'spent'and therefore effectively 'null and void'. However the police will still have it on their databases for life. They of course are not able to divulge that to anyone, (Unless a private detective greases the right palms of course).
Thus you will have to declare it on a job application, and if it was only for a minor 'one off' transgression your best plan is to put 'Discuss at interview' in the box related to convictions in the hope that your other qualities shine through enough to get you through the front door. Then you have the opportunity to tell the facts of the case and downplay the whole thing.
As far as the CAA are concerned, the medical form no longer asks for information about convictions. It used to, but I noticed the last one didn't. Whether they still require it for initial issue I don't know. Generally, I have found the CAA to take the view that if the crime is for an offence unlikely to be repeated in the air, then they take no action. Thus, for example crimes leading to violence on the ground such as night club punch ups or marital disputes are not immediatly blocked as the stimulus to reach such levels of anger are unlikely to be provided at work. (Mind you they havn't seen me and Greek handling agents!!)A drink drive conviction is not likely to be a problem if it is truly a one off, but a history would certainly raise interest from the CAA.
In times of dire pilot shortages I have even known of a pilot being approached in prison to see if he would like a job on release. (No not me!)
It all comes down to supply and demand. The bigger operators will take a stiff attitude to anything that deems to 'let the squadron down'! So you may find it hard to make the larger jet operators. But at the end of the day if you fit in and the company like you, then all this will slip into history over time.
Generally, I would say don't be too down hearted, but in the present economic climate I woudn't advise anyone to spend vast amounts on training until the economy picks up.
Incidentally I know of one First Officer that joined a UK charter operator with a fresh drink drive conviction, witheld it, flew for a year avoiding the need for using hire cars, and has now gone on to another airline. So it can be done, but I woudn't recommend it as if you are found out the 'internal network' between UK operators will ensure that the African market is about the only place you'll be likely to get a job.
Good luck in the mean time.