I'm no expert at searching Hansard and no doubt someone with those skills will be able to find more relevant information, but I did find these quotes from the House of Lords debate on the 7th of July 1981 regarding the British Nationality Bill.

From this debate, at least, it seem that the Government were concerned about people who were in the UK without permission having children who would automatically become British citizens, and they were interested in harmonising nationality law with the rest of Europe. The opposition were concerned that the change would be a break with a very longstanding tradition, a break with the rest of the Commonwealth and that the government had some racist agenda behind changing the law.

Lord Home of the Hirsel:

As I said at the Second Reading of the Bill, and I shall not repeat it except in shorthand, there are now people in the Commonwealth and outside it who are conducting a profitable business in illegal immigration and who are conducting it quite successfully. A good many illegal immigrants are in this country today. As we all know, thousands of tourists and students visit this country every year or stay in this country for a number of years on a scale which was totally unknown only a few years ago.

My noble friend on the Front Bench, Lord Belstead, will correct me if I am wrong, but according to the amendment as it stands the son of an illegal immigrant who has taken the trouble successfully to cheat the immigration laws would, as I understand it, be able to rely on the fact that his son—and not only his son but his grandson—would be able to claim permanent citizenship of this country. That is a proposition which I think will outrage the ordinary citizen who is here legally as a citizen of this country with a right of abode.

In these days of mass travel there are very large numbers of students. If again I am not wrong, let me take as a practical example a boy and a girl coming from Iran who have a child or a number of children. Those children would automatically, in the words which were used by the noble and learned Lord, Lord Elwyn Jones, be citizens of this country—and not only they, but their children in turn. I am all for elasticity in the law, but I cannot really see anything in Christian morality or common sense which dictates that such children should have permanent citizenship of this country.

Lord Hunt:

We have heard that the Government's intention in abandoning jus soli is, in part, on the grounds of the transients, the tourists, the students, the overstayers, the illegals, and the children whom they may produce while they are here. We have not heard so far—maybe the Government will produce some figures—any statistics. The noble Lord, Lord Home, said large numbers—presumably meaning large numbers of children—born to these categories of people. But we have not heard statistics, nor have we heard of any trouble over all the hundreds of years that have passed, nor, more importantly, in the very different world in which we are living today. Nor have we heard—I should like to know whether the Government are concerned about this—about how they see the future; whether they really see the retention of jus soli, if this amendment were to succeed, going into the Bill and becoming law, resulting in a sudden ingress of pregnant women coming to this country for the precise purpose of having their children here and passing on the convenience of a British passport in later years to their children.

Lord Belstead:

The noble Lord, Lord Avebury, again in a most interesting part of his speech, gave examples of countries around the world which retain the jus soli principle. I listened as carefully as I could, but I did not discern in the list which the noble Lord gave very many countries which bore much relation to the demography and the logistics and the general society in which we live in this country today. In Europe, of all the 10 countries of the European Community there is one country, and one country only, which does what the amendment moved by the right reverend Prelate would wish us to do, and that country is the Republic of Ireland. All the other countries of the European Community today require the parent to be a citizen before citizenship can be transmitted to the child, and in many countries it is only the father who can transmit. By comparison, Clause 1 provides that there will be no sex discrimination in our nationality law. For the first time children would be able to take their citizenship from their mother or their father, and unlike most countries relying on citizenship requirement for acquisition, Clause 1 also says that if the mother or the father is settled in the United Kingdom that makes the children citizens by birth.