Yes, up to a point, although it is going to be difficult to pick through the minutiae without having to write a history of post-war British education.

In February 1974 it first raises its head:

All forms of tax-relief and charitable status for public schools will be withdrawn.

but by October 1974 the manifesto included:

Stop the present system of Direct Grant Schools and withdraw tax relief and charitable status from Public Schools, as a first step towards our long-term aim of phasing out fee paying in schools.

This was carried out, although Direct Grant Schools are not what most people think of when they think of "public schools". Direct Grant schools were historic independent schools, most of them day schools, which had been funded as extensions of the grammar system in the aftermath of the 1944 Act. The removal of that funding was enacted very rapidly, and direct grant schools took no further state-funded pupils from 1976 onwards, becoming pure independent schools again. This was more about dealing with some of the manifest injustices of the 11+ than public schools per se; direct grant schools has operated as a shadow 11+ system even in authorities which had merged grammars and secondary moderns to form comprehensive schools, and were very much occupied by the privileged middle classes.

The issue is raised in stronger terms in the 1979 Manifesto, the election that brought Thatcher into office, although with little detail:

Independent schools still represent a major obstacle to equality of opportunity. Labour's aim is to end, as soon as possible, fee-paying in such schools, while safeguarding schools for the handicapped. Labour will end as soon as possible the remaining public subsidies and public support to independent schools.

The first manifesto to aim serious at the public schools in 1983, the "longest suicide note in history". The assisted places scheme was another middle-class subsidy, which was brought in by the incoming Thatcher government and then absolished as one of the first acts of the Blair government in 1997.

Private schools are a major obstacle to a free and fair education system, able to serve the needs of the whole community. We will abolish the Assisted Places Scheme and local authority place buying; and we will phase out, as quickly as possible, boarding allowances paid to government personnel for their children to attend private schools, whilst ensuring secure accommodation for children needing residential education.
We shall also withdraw charitable status from private schools and all their other public subsidies and tax privileges. We will also charge VAT on the fees paid to such schools; phase out fee charging; and integrate private schools within the local authority sector where necessary. Special schools for handicapped pupils will retain all current support and tax advantages.

It is not clear to me now (nor was it at the time, when I was in the Labour Party and rather more of a firebrand than I am today) what "phase out fee charging; and integrate private schools within the local authority sector where necessary" actually meant. Had Labour come to office in 1983 we/they would rapidly have found that removing the opportunity for people to both pay income tax and then voluntarily also fund the full cost of their children's schooling leaves a massive financial hole in the education budget. At the time, around 12% of children were privately educated for some or all of their 5-18 years, and even if you nationalise / sequestrate the buildings, you still need to pay the staff. An increase of 14% in the number of places to be funded, without a penny of additional revenue, would have been doomed, even had there been sufficient qualified teachers available.

Why the shortage of teachers? Working in the state system requires staff to be qualified teachers, with a PGCE, a B.Ed or a Cert.Ed. The private schools were not so constrained, and then as now employed a lot of staff who had first degrees but no teaching qualifications. Had those schools been taken into public hands they would have had a lot of staff who were not qualified to teach in state schools, and no obvious reservoir of replacements; because of the raising of the school leaving age in 1972 there was already massive pressure on staffing in secondary schools. It could have been fixed, but like most of the 1983 manifesto the details had been drowned out by the fervour.

By 1987, the policy had been substantially watered down and is mostly again about the 11+ and the Assisted Places scheme.

These policies [[ ed: other education funding policies ]] will all contribute to raising standards of performance in schools. At the same time as we improve the quality of publicly provided education, we shall end the 11 plus everywhere and stop the diverting of precious resources that occurs through the Assisted Places Scheme and the public subsidies to private schools.

And similarly in 1992, it's just the Assisted Places scheme.

Nine out of ten secondary school children are in comprehensive schools. We will end selection at 11 where it still exists. We will introduce a fairer system for all school reorganisations, with independent public enquiries. We will phase out the Assisted Places scheme (without affecting pupils currently on a place, or offered one from September 1992) and redirect the savings to meet wider educational needs.

And by 1997, aside from "We will reduce class sizes for five, six and seven year-olds to 30 or under, by phasing out the assisted places scheme, the cost of which is set to rise to £180 million per year." (ie, the assisted places schemes' merits are secondary, it's just too expensive and a source of revenue for doing something else) it's pretty obvious which way the wind is blowing:

Labour will never force the abolition of good schools whether in the private or state sector. Any changes in the admissions policies of grammar schools will be decided by local parents. Church schools will retain their distinctive religious ethos.

And after that, the issue has lain pretty much fallow other than in the fever dreams of the hard left, and even then the 2019 manifesto is back to the tax advantages (which are, I am afraid to say, mostly illusory -- businesses whose main costs are buildings and staff are very low net VAT payers) and some vague stuff about a social justice commission "integrating private schools".

I doubt that a Starmer Labour party is going to touch it, and I think the issue is pretty much dead. Mind you, given the current demographics of independent schools, I suspect the imposition of sanctions on Russian banks is causing some sleepless nights for the bursar.