Closely look at the individual situation and at section 7 of the deer act. Is there serious damage to fruit or cereals or growing timber, as examples (not just limited to those, look at the act). Can you gather and file photographic evidence. Not only this but can you pin down the species in question and get evidence of that species doing this damage. Have other preventative methods been exausted. Why aren't the numbers being dealt with in the season. If yes, the guy will need to say in writing and give you authority under sect 7 of the deer act , to cull the species in question for the damage being caused to whatever it is that is applicable in that instance. A letter perhaps separate from the landowner also talking about the damage caused and the monetry value lost in the past year due to the species. Keep that file with all of this, on you at all times, in a backpack or whatever. If you agree to do it, that is the only way how and it isnt a free for all, if stopped for doing it.. it is a defence and you will have to explain yourself in full. I have no idea if this has gone to court or been tested etc etc. The act isn't ultra specific in how exactly, to the letter, you defend your actions. Place yourself in the position of a knowledgeable police officer or wildlife crime officer that stops someone and asks why they have a dead out of season animal and what would satisfy you as evidence and defense..
For anyone just saying its a no go, section 7 exists for a reason and serves a purpose. It is a niche purpose but a purpose nonetheless and it is why it exists, you just have to be serious about it and how you go about it. In many cases it can be avoided but in some, its hard to avoid also.
However with the laws changing, like they have in Scotland, what with last years English consultation on deer... it may just be worth saying everything you would need to do above and say it holds risks still and politely explain due to the risks, it may be better to wait a short while and stick to seasonal for now because England's deer laws may well be changing anyway. The law on male deer may be extended indefinitely and night shooting laws may be laxed in some respect.. (but we won't know this for some time) giving you more time to cull species that are in season and giving 50% more access to species that were previously completely out of season i.e males not females. If that makes sense. And as rightly mentioned above, from November does are in anyway, if we are talking about now and not generally future reference.
Talk to Basc's deer department if you are a member. What you want are cold facts. Forums aren't good places for legal information... it is mostly opinion/conjecture and not facts all that often. Always print and keep whatever advice is given in writing/email from your shooting legal advisor, whatever organisation gives it.. I do.