In short, yes and yes (though not directly).
First of all, allow me to say that although it does appear as if your boss is not the perfect boss, you are truly being the issue. Forgive me for saying it so directly. Consider your attitude, and pay attention to the wording when reflecting on what you wrote yourself. I've added some emphasis:
Me [and my boss]...
Certainly, it is not all uncommon to say "me and my boss" rather than "my boss and me" in English. In other languages, it is considered outright insulting and obnoxious in a slap-face way -- in English not so much, admittedly. But think about it. Really. Who is to be named first? It's a subtle hint to what may be the issue.
We often argue about the morals and future of the company..."
There we go. Be honest, who is the one entitled to have an opinion about the morals and future of the company? The boss, or you? Sure, a good boss will (may) listen to what his employees think. And failing to do so, he is maybe not the best boss in the world.
However, in reality it's you who is inherently wrong and inherently showing the wrong attitude. The future of your company (which your boss owns, not you) is not yours to decide or argue about. Constructive feedback is acceptable when welcome (but not acceptable when not welcome). Arguments are never acceptable.
Yes, you are allowed to have an opinion, and you may even have freedom of speech in your country. That, however, doesn't automatically mean that you have freedom of speech at work, or that anyone (your boss included) must listen to what you say, or that you even have a word in business decisions.
Similarly, you are for example allowed to freely exercise religion (pray to God or Allah, or whatever you like). But that doesn't mean you are allowed to lecture and convert your coworkers about The One True Belief. You are not allowed to preach at work and tell people that they pray to the wrong thing. It's very much the same thing. There's things that you are generally allowed to believe, or say, or do... but not at work. You are allowed to think that your boss is a complete asshole and that his decisions are utter bullshit, and you can tell your girlfriend at home. But you may not say it at work. You may think that a business decision doesn't make sense, but you are still required to follow it.
The same is true about your boss spending company money for himself. Well yeah, what about it? It's his company, and his money. You do not have a say in it. If you think you do, you must get your perspective right (or else you will have trouble with your next employer, too).
Now, that's a general thing, but now about the actual issue.
About what you've really done wrong, which is why your boss is in fact entitled to fire you and will (most probably) get away with it. Yes, you have rights when being dismissed, but your employer has a valid reason and has acted reasonably, and they have a demonstrable, vital interest in doing the dismissal immediately. Insofar there will likely be not much (if anything) you can do.
This is something that I seem to repeat twice every week to different people: You do not only have rights, you also have obligations!
Being truthful is an obligation. You called in sick when you clearly weren't sick (and you were unwise enough to "announce" it by first asking for a day off because you had tickets, etc etc). This is absolutely, totally, completely, 100% inacceptable.
There's not even much of a way you could fix this mistake, even if you wanted to. Because, well, it's not about taking a day off. It's about betraying your employer's confidence.
This is a huge problem, and it justifies what your boss has done.
Reasoning: If you are fraudulent about being sick, you are probably fraudulent about other things, too. You probably charge overtime hours that you haven't done. Who knows, you might embezzle company money if given the opportunity. You might steal work equipment or money. You might cause damage to the company just because you are being spiteful.
Note that I am not saying you actually did any of the above. But you get the idea. This is serious.
Additionally, you did not comply with the request of confirming that you have received the invite. So, in addition to violating trust, you have also undeniably committed a formal mistake (noncompliance to a direct order). Which is, well, just another nail to your coffin that demostrates your consistent (not exceptional!), misbehaviour. Yep, he lured you into that one, and you fell for it.
Therefore, while your boss cannot (at least not easily) fire you immediately, he can very well fire you within the usual period and at the same time suspend you, and order that you leave his grounds, effective immediately. And he'll get away with it, since you've provided the necessary evidence of persistent, irreconcilable differences.
Which, if that's not the exact wording of your notice already, you will be explained when trying to challenge his decision.
The approach of effectively "firing immediately" is not even unusual, a lot of large corporations do that exact thing (and worse!) when they lay off someone. Security shows up at your cubicle. You, being completely unaware, are handed the notice, and then security leads you out, and that's just it. End of story. Yes, technically you're employed for anther two weeks. In theory.
They're not giving you an opportunity for a little revenge operation. They're not giving you an opportunity to walk out with trade secrets. They're not giving you an opportunity to incite a little rebellion at work. No Sir.
Can your boss deny writing a recommendation letter (or testimonial)? Seeing how you are in UK, yes. You simply do not have a right to receive one.
But even if you were in another country where you have the right of getting a testimonial (e.g. Germany), he could deprive you of that right (and of the other related rights as well) if he wanted to. The reason being that while you have the right (not in UK, mind you!) to receive a testimonial (truthful, and not negative), it is your responsibility to come and get it. There is no obligation to send it to you. See where this is going? If you are not allowed to enter the grounds, how are you going to get your testimonial?
Similarly, the employer is required to write a truthful, non-negative testimonial. But he is not required to write a positive testimonial with the well-known superlative positive clauses. Other employers obviously know that, and a testimonial without said clauses is factually a negative testimonial (without being such).
So, even in countries where you do have a right of testimony, unless your boss is a completely incompetent idiot, this is a fight that you cannot win. You do not want to go that route.