You've left this too late. There is no cheap or risk-free option. If they are serious about defending their rights and not just throwing idle threats around, then you could end up paying an awful lot of money.
- The employee has been underperforming and you have not properly addressed this matter, you've declined give him warnings, and relied on 'informal chat'. There's a right way to go about things and you haven't done it. Under UK law, you don't get to opt out of giving people a fair hearing (even angry, lazy people) just because you don't want to - it's what you sign up to implicitly as an employer.
- The employee has two years' service, which means they're entitled to claim unfair dismissal if you don't follow a fair procedure, e.g. as laid out in the ACAS Code of Practice. Don't try to sack him just beforehand if you discover he has only 23 months, tribunals can see through that and have wiggle room.
- You are already vulnerable to a claim in an employment tribunal if you dismiss him, as you have clearly already made up your mind, and any procedure you now enter into is probably a sham. You might manage to get an external HR company to help organise a fair hearing; they may well advise you to hand over the decision to a third party. It's rare that this happens; and you'll need to be willing to accept the decision, which may well fall short of dismissal.
- More likely, you will probably want to offer a settlement agreement (previously known as a compromise agreement). Again, you absolutely must get someone level-headed and uninvolved to do it who knows their stuff, as doing it wrong would lay you open to a claim. An external HR company would do it, and ACAS or the FSB might be able to advise you. If your priority is to get him out the door, that will cost more: ask yourself, how much you'd pay to not have to deal with the hassle any more - that's your offer. If he's really as bad and litigious as you say, that's probably quite a lot. Don't assume the employee will accept the offer. You need to be ready to deal with the fallout if they don't.
- Even if you rashly fire him on the spot and risk a claim, you will almost certainly need to budget for paying the notice period, which would be a minimum of two weeks, plus any unspent holiday, etc.
Without knowing what the employee might claim should you dismiss it's impossible to give more specific suggestions or any idea of the strength or size of a claim; in any case, we can't give legal advice on this site. Ask an expert without delay and be prepared to pay for it.
Even if this particular employment relationship is unsalvageable, try to think through this from the employee's point of view when you handle situations like this in the future.
They probably don't know you're planning to fire them, or that that's even remotely likely. They probably just think you occasionally want to vent your own anger by having a go at them, and that there's no problem at all. They certainly haven't been given the time and opportunity to get their own expert help in (e.g. their union rep) to help repair the situation, understand what needs to change etc. Now some people might not want to engage with a process - that's fine, but you don't know until you try.
All your employees need to know about problems as soon as they happen so they can make a difference for both your sake and theirs. And all your employees need to feel confident they're doing well, not just that you're just avoiding having the difficult conversations with them. Finally, when you bring in a replacement, set standards, review with them what has and hasn't been met early on. The earlier you address problems, the better.