Hfrhyu

Does Parliament hold absolute power in the UK?

What I mean by absolute power is: presumably they can make illegal or legal whatever they want. Even going so far as to disenfranchise their own electorate.

Is this correct, or are there any checks on the power of Parliament?

Parliament has one power. It can pass motions.

These motions can become Acts of Parliament and define new laws. The text of the Act of Parliament is basically unlimited. An Act of Parliament can, in theory, consist of nothing but the word "Rhubarb" written 5000 times. It could contain a statement that "pi = 4", or it could repeal the law of Gravity. These are silly examples, but they show that Parliament can create any act that it chooses. How that relates to "power" is more questionable.

Obviously, an Act that declares "pi = 4" would have no effect on the actual value of pi. Similarly an Act that is unenforceable, will not be enforced.

Could Parliament change the electoral system to vary who gets to vote? Yes they have done this multiple times in the past. The direction of history has meant that the franchise has been extended each time, to include non-property-owning men, and then to include some women. But it is far from the case that "everybody" can vote. Prisoners, under-18s, and The Queen, for example, have no vote in elections. Parliament could make it impossible for women to vote, but such a law would be unenforceable.

The ultimate check on the power of any authority is the risk of violent revolution. This restriction on the power of any government is implicit.

There's a substantial difference between the theoretical and actual limits of authority held by Parliament.

De facto

In the UK tradition Parliament's authority is theoretically absolute. With a sufficient majority in the House of Commons any law can be passed and the authorities (police, judiciary, etc) can be directed to enforce that law. The upper House of Lords can attempt to delay or amend those laws, but the lower house has primacy and can force them through after a certain amount of time.

De Jure

All new laws must be 'assented' to by the Monarch. Since the Parliament are (again theoretically) subject to her failure to assent, the 'in law' position is that Parliament is not absolute since the lower House of Commons can't direct her to sign even with a majority vote. In fact, without her specific consent to form a government and sit in session, Parliament is dissolved.

Realpolitik

In the real world, Parliament is bounded by a great number of limits; the need to secure a majority in both houses for normal legislation, the enforcability of laws that are passed, budgetary limits, EU law (for the time being), International Law, various treaties to which the UK is signatory and pressure from outside bodies with influence (such as foreign governments).

Another elephant in the room here is the European Convention on Human Rights, an international convention to which the UK is a party state. This effectively gives a supranational body, the European Court of Human Rights the power to pass judgement that a contracting state has breached provisions in the convention concerning human civil and political rights.

The original treaty does let states leave (denounce the treaty), but only after a 5 year cooling off period. As with all international treaties, it's not entirely clear what would happen if a state just unilaterally stopped playing ball immediately, especially if it were willing to enter a period of North Korean style isolationism, but it is another element in play, beyond the various parties (and the two houses) of Parliament watching each other.

The Fixed-term Parliaments Act means they have to respond to the electorate, eventually. In fact this provision has existed for a long time in various forms

The Septennial Act 1715 provided that a parliament expired seven years after it had been summoned; this period was reduced to five years by the Parliament Act 1911.

The House of Lords can exercise some restraint in terms constitutionality of laws, although given the lack of a single, written constitution in the UK that's a complicated exercise.

Presumably the Queen can withhold Royal Assent on some completely insane law, but there isn't much in the way recent precedent.

The last bill that was refused assent by the sovereign (on the advice of ministers) was the Scottish Militia Bill during Queen Anne's reign in 1708.

Just to add to the other answers here, in theory the monarch can veto an Act of Parliament by refusing Royal Assent.

In practice Royal Assent is a formality and the theoretical power of veto is never exercised. The last time Royal Assent was actually withheld was in 1708. However if Parliament voted to do something so clearly undemocratic as arbitrarily cancelling elections or disenfranchising the majority of the population then it remains a possibility.

Also relevant is the fact that the UK monarch is the head of the armed forces. In theory the Queen could order the army to go and arrest the Prime Minister, and it would be a legal order that they would have to obey.

(An urban legend has it that Queen Victoria withheld assent to a law outlawing lesbianism on the grounds that no woman would ever do such a thing. This is not true.)