I've worked with the one of the biggest and best known firms in the UK. They are very expensive and very good, but I would just advise that you take a step back for a second before you rush to the lawyers. They will break you financially, so here's some free love (UK only I'm afraid).
TL,DR; this threat is worthless. Don't fret about it.
In the UK such letters are no more than empty words, in all cases without exception, the onus is on the writers to bring something to court before they can be awarded any money and that requires you to have breached some specific point in law. So let's ask the question, "what exactly can they do?" what law did you break? What evidence do they have that you broke the law?
I'll put it bluntly, this is blackmail they can't do anything without it costing them first a huge amount of money and time, and their chances of success are very small.
Look, their laywers probably said, you haven't got anything. If you like I'll write a stiff letter. They haven't actually broken the law, but the letter may just work.
Let's deal with the first point. As far as defamation is concerned, the fact is you did not write the posts. You cannot be held liable for what was written. The fact that you host the forum is not a related issue, and it cannot be implied that because you own the site you are responsible for every word - they would have to establish a legal case that somehow you (and every other website in the world) is legally bound to police the content. That's basically it.
Your defence: You should always take a position that is removed from the issue so as to not directly link yourself to the issue.
As far as I can see, the posts are probably in breach of your terms, and as the owner of the site you have a perfect right to decide what stays on and what comes off your site. The best course of action here is to say that you have looked at the posts as soon as you were made aware of them following this letter and agree that they breach your terms, and have removed them. That's the very most that can be expected and their lawyers will have advised their clients so. They would also advise their clients that pursuing this further is a waste of money.
Do not apologise under any circumstances as that would be an admission that you are somewhat implicated.
Do not even address the point about "doing it again" - that's just bull. It's a trap - do they think you're stupid?
Damages? They have to provide cast iron proof that they have been financially damaged. This is almost impossible to do in cases of defamation, and they would have to prove it to the judge. The judge will likely award zero damages, so do not address this point.
In the UK you are only obliged to pay another person's legal fees if the judge orders it (meaning it has to go to court first which it won't) and the basis on which this order is made is if the other side can prove that you have acted unreasonably (a very very difficult thing to do in law, because it relies on legal precident of which there are very few examples). You will pretty much have quashed that (being unreasonable) argument if you just remove the comment. They could never claim that you had acted unreasonably, and even if they did try to claim, it would be very very very unlikely to succeed. Judges rarely award costs especially for something like this where the letter seems to be a kind of extortion.
But... even if a claim for costs did succeed it still doesn't mean you have to pay. Here's the crazy bit....
The costs award is open to negotiation, and further still if you refuse to pay the costs (which you are perfectly entitled to do even if you've been ordered to pay costs) the other party then has to take you to court again (it's called the high court for costs) That's more money for them to spend and they can't get "costs for recovering costs" hahahahhaha
Even then they have to win at costs court, and you can force them to lose with a series of offers which will result in them having to pick up all their own costs anyway. Costs judges are very strict on what is allowable and it's always in your favour to have them look at costs because they throw out a whole load of stuff that can't be claimed - much to the annoyance of the people hoping to get their costs paid for!
So put yourself in their shoes - it's going to cost a whole heap of dough just to prove that you somehow influenced the writer, then a whole heap of dough to try to prove that you've been unreasonable in dealing with it. So what are the odds of their success?
Revert for fun.
One last bonus for you. Lawyers are generally fair players - meaning that they won't act whilst the other side is in the process of replying, it's only fair. So if you send a reply, simply "ackowledge receipt of the letter and will revert in due course".
That's real fun because their lawyer will say to them that they can't do anything until you've replied, which could be .... NEVER ....
This all sounds like games, but it's not personal, just business, and this is the of stuff you can legimately do to get these sort of shisters off your back. And it costs nothing except a small bit of time.