I won't repeat what others have said, but I think they are very likely to be correct. Plymouth has made forces even more risk averse and, if media reports are to be believed, they are revoking certificates for things which arguably should not lead to a revocation (to be clear, what you describe should).
The best person to speak to is your local FEO, and be frank about the circumstances of your offences. If you play them down to get a positive answer, don't be surprised if when you actually apply the response isn't the one you expected. I wouldn't expect them to give the ok at this stage (and, for what it's worth, don't think they should), but you might get some pointers about how to get yourself into a position to be considered, and how long that might take.
Also keep in mind that the FEO can look at all circumstances, which includes suspicion of offences as well as convictions. Given you have been convicted of drug driving, there is an inescapable conclusion that you have also possessed drugs.
It is also worth having a think about the circumstances of your offences (I'm not suggesting you put them on here) but if your drink driving was only a little over the limit it may not cast the same doubt on your character as if you were double it (for example) or if it followed a lengthy police chase. To be clear, I'm not suggesting being a little over is ok, it isn't, only that there are things you could do to make it even worse.
As others have said, convictions are never spent for these purposes. However, putting some time between the offence and application can't hurt as it might allow you to say that you have learned from your errors. Were I in your position, and I really wanted a license, I'd have a serious think about why you found yourself in the situations you describe and then work out how to ensure those situations aren't repeated, e.g. keeping bad company, not having the right coping strategies etc. It can't hurt if, in some years time, you can explain to the FEO why you made those mistakes and why they won't be repeated because you've addressed the causes.
In any case, you will always be on thin ice. If you do manage (in future) to get a license and repeat anything like that behaviour, I can't see you being granted any leeway at all.