Currently (and I stress that word), you can move to any EU country and you have the automatic right to live, work and retire there. You can get "permanent residency" after living uninterrupted for 5 years in an EU country, but you can still legally live there right now if you wanted to.
If you are subject to any specific orders/notification requirements in the UK, it is subject to the UK authorities/Probation/police etc. giving you the all-clear to go and live abroad. If you're not subject to any of these conditions, then you're free to go and live and work anywhere in the EU - for the moment! Go sooner rather than later if this is your serious plan.
Some EU countries have fairly low requirements for eventually gaining citizenship - thus EU citizenship post-Brexit - e.g. by simply living in that country for a certain number of years (5, 7, 10 ... depends on the country).
Independently from the EU, British citizens have automatic and unlimited right of abode in the Republic of Ireland and enjoy quasi-citizenship status, i.e. they can vote in all elections (except presidential elections and constitutional referendums), work there with no restrictions, and are entitled to all the benefits as if you were an Irish citizen.
Lastly, some countries in the developing world (mainly Africa and poorer parts of Latin America) have lax systems for checking criminal records, and don't even ask about convictions on visa forms. But you would probably need a job there to be allowed to live there - I'm not sure you could just move there because you felt like it, like you currently can in Europe.