The Lords can veto Parliments proposals, in fact they just did so in two laws the new Uk government wanted to introduce.
Unfortunately, the editors of the Encyclopædia Britannica don't agree with you:
Under the 1949 act, all other public bills (except bills to extend the maximum duration of Parliament) not receiving the approval of the House of Lords become law provided that they are passed by two successive parliamentary sessions and that a period of one year has elapsed between the bill's second reading in the first session and its third reading in the second session.
britannica.com/topic/House-of-Lords
Delaying the passage of a law for a year is not the same as a veto. It simply delays passage and is best described as "cooling saucer" of public sentiment and is clearly not as permanent as a veto, or the refusal to grant royal assent (which never happens in the U.K. anymore, and hasn't happened since 11 March 1708 for the simple reason that it is overtly anti-democratic). Rejection by the House of Lords is simply an embarrassment to the government in the Commons, like farting in church.
In the UK there isn't a explicitly written constitution.
In the UK there is no actual constitution. It is an imaginary thing, not the least because no method is known for amending what doesn't exist. If there were one, we could all read it. We can't so you are writing nonsense.
The law is set by politically independent judges who politicians must answer to, legal precedent is used as the basis of their judgement.
The law is set by the House of Commons according to the doctrine of Parliamentary sovereignty. The judges then attempt to determine what the legislature intended only if two laws conflict, like the law accepting admittance to the EU with subsequent laws which must be disapplied when they conflict. The politicians in the Commons answer only to the electorate, not the judiciary. (Although the same is not true of the legislatures created by the commons by "devolution".)
Since you, (and others posting here), are ignorant of the laws and political relationships between your own political organs, how do you attempt to pass judgment on those of foreign nation?