The short answer is there's very, very few jobs to be had in agriculture in the first place. To remain viable agriculture has had to go one of two ways, either bigger and more mechanised, or relegated to part-time with the owner/occupier doing everything.
Dairy farms would have bit your hand off even as recently as 15 or 20 years ago, but even they now have had to consolidate and minimise labour to survive, and there's only three of them left now anyway.
Right now is probably the worst time in the last 20 years to be looking anyway, agriculture has been operating in a manipulated and artificial marketplace since we joined the EEC/EU, that will change with Brexit, but with a useless Government who've given minimal indication of what their agricultural policy will be post Brexit, and done less still on getting our imports/exports post Brexit to work for us, nobody has a clue whether we're heading for boom, bust, or just SSDD, and are playing as safe they can with costs and investments as a result. Including just making do with who they already employ at the moment, and waiting to see how things go before deciding whether they can justify any additional cost committments.
If you're in a position to consider part-time casual work, that can be a good way to get a foot in the door, and there are folk who will hire you for a limited period, or for the duration of a certain job, who cannot justify a permanent position. Once you're known to anyone in the industry, and they're happy with your work, the internal networking makes getting further employment much easier as folk in the trade talk with each other and names get passed along.
Having your own transport is vital for casual work though, and some level of experience is close behind it. Yes, I know, you can't have experience unless someone gives you some, and without it its difficult to find someone willing to take you on to get it.
If you know people who are already involved in agriculture, talk with them periodically to see how things are and if they're aware of anyone looking to maybe hire someone, and try approaching owners of some of the bigger places. Most will have everything covered already, and be prepared to have to try and talk anyone who might have an opening in to hiring an apprentice, as if they've not already decided the apprentice route is the one they want to go with, initially at least they're very liable to dismiss the idea, as just about everyone would rather hire someone who already knows the job than train someone up.
Its only when they sit down later and crunch the numbers of what someone who knows the job is going to cost them, and how realistic it is to find and keep such a person, that sometimes taking an apprentice suddenly makes a whole lot of sense.
You may well feel you're fighting a losing battle at first, but once you've made contact with a few, your face is out there and you'll be remembered in the future if something does come up.
Don't blitz all the bigger places in one go, select a shortlist of a few, see how it goes, then repeat with another shortlist in a few months. Around now is good, as folk have spring work, lambing etc on the go, and may need an extra hand through that, June/July folk often need someone extra for silage, nearer the autumn sometimes assistance is needed with livestock handling and shipping out etc.