The monarch can refuse to sign legislation. However the refusal to sign would trigger the dismantling of the monarchy plunging the UK into a deep constitutional crisis not seen since Oliver Cromwell.

And while technically the House of Commons can pass just about any law it wants, the House of Lords generally acts as a counterweight to reign in worst of the Commons. Usually if its not in the governments manifesto and the bill gets kicked back to the Commons then by convention its usually kicked into the long grass unless the changes proposed by the Lords are acceptable.

Of course the Commons could invoke the Parliament Act to push through legislation it generally only does so in rare circumstances (a handful over the last century). However any attempt to do this over anything other than a firm manifesto pledge would likely again plunge the UK into said constitutional crisis.

So the checks and balances in the UK system come from the fact none of parties involved wants to deal with the mess that would result if they didn't follow prior convention.