Wherever you search you will need the landowner's permission. Technically speaking anything you find is the landowner's property. They may agree, possibly in advance, that you can keep your finds but you need to be mutually clear about this.
If you are searching on a nationally or locally listed monument eg a battlefield or a Roman fort, you will need permission from English Heritage as well as the landowner. If you make contact with your local museum they may be able to put you in touch with a group who will help you make a good start and avoid the pitfalls.
Digging for objects is hard work, even in a recently ploughed field, so why not start of on a beach? Permission can be very easy to obtain (mostly nobody's bothered) but as well as having easier digging it is where eople drop money and jewellery. And sometimes rare archaeological artefacts turn up on beaches. Oh, and mines. Seriously.
If you find archaeological material you must report it correctly, hence your need to link in with a group from a museum who will help you do this.
Enjoy - but avoid the mines.