Note: I'm assuming OP lives in the UK, judging by their name and reference to London.
Let's get the answer that you want to hear out of the way- no, a company cannot terminate you without cause and resigning is not a valid cause. Sometimes an employee will be asked to leave immediately rather than working notice but in that case they are still paid and technically employed (this is known as Garden Leave).
Lets also ignore your comments about how you think your boss is a jerk and try to vaguely imply that he's embezzling money. Even if that last part were true, which it isn't, it's irrelevant here.
The circumstances under which you can be fired will be in your contract, and probably available in an employee handbook. They will include some variation of "Gross Misconduct". Missing work without a valid reason will likely count and faking being sick certainly willespecially if you lied about your reason. Resigning does not magically protect you from termination.
tl;dr- You were in the wrong here and have no legal recourse.
You are correct that you shouldn't ask your boss for a reference. Depending on the size of the company and its policies, you may be able to get around this by getting a reference from another manager, such as your line manager if you didn't report directly to your boss.
You should probably try to get this question dissociated from your account, since I'm assuming that's your real name there.