For data protection reasons, your employer wouldn't find out about it officially unless you agreed to tell them.
Ask your HR dept for a copy of your contract and for a copy of your handbook (as something about criminal activity might not make its way into the contract but would be more likely in the handbook - which normally is part of the contractual agreement).
However, I would suspect that unless you work in a role where they have grounds for not employing people with criminal records - in some roles where you might work with kids or the elderly or if you were in charge of money in a senior role - then they shouldn't get rid of you for it.
The only exception I can think of is if for some reason the fact you work for them and this happened to you becomes public knowledge (for example, reported in the press) and they ditch you for bringing the company name into disrepute.
For future roles, you are normally asked about convictions under the ROA act. I don't think cautions come into it. Look up the terms of the Rehibilitation of Offenders act for clarification on that.