Not very significant. The UN Special Rapporteur has no actual powers to effect change, as set out in the mandate given in RES/48/14.
Firstly it's worth noting the the Just Stop Oil protesters were not sentenced after a peaceful march. As your link points out, they blocked the Dartford Crossing for over 40 hours, at great risk and expense to the public, themselves, and the emergency services who had to remove them from the bridge.
Andrew Tettenborn, Professor of Law at Swansea University gave the following reasons why it's not surprising that the UK government apparently chose not to give much weight to Mr Fry's letter:
For one thing, it’s a bit difficult to see the connection between the freedoms of expression and assembly mentioned in Fry’s letter and the deliberate act of inconveniencing as many people as possible by blocking one of the country’s busiest roads for nearly two days. The reason we value free speech and assembly is precisely that they are non-invasive: they seek to persuade, not to coerce. If the Covenant on Civil and Political Rights is now to be interpreted as requiring democratic governments to allow aggressive pressure groups to impose their views by force on the public whether their electors agree or not (which is doubtful), one can hardly blame the UK government for not being over-keen on obeying it to the letter. The government has every right to see this as an impertinent attempt by an international apparatchik to intervene in the detailed internal administration of this country of a kind that needs to be resisted hard.
Does it matter that the UN seems to be becoming increasingly foolish, selective and, frankly, irrelevant when it comes to matters such as free speech? Actually it does. There are plenty of states guilty on a regular basis of serious and violent suppression of dissent, including those guilty of nothing more than ordinary, non-coercive speech or membership of non-violent campaigning organisations. The UN retains the ability to do a great deal of good for freedom and world peace in such cases.
If so, however, it needs seriously to avoid frittering away what respect it still retains by intervening in the case of vociferous but undeserving organisations like JSO. The members of the Human Rights Council who control the appointment and activities of their special rapporteurs have the power discreetly to rein them in. They would do well to recall this. On the question whether the UN can remain as a credible organisation in the field of civil rights, the choice is, one suspects, largely theirs.
By way of comparison, Mr Fry's letter is far less significant, for example, than the UN's special international maritime court ruling against the UK in the case of the Chagos Islands back in 2021. In this scenario as well, the UK was under no obligation to comply with the ruling, as the UN is in the majority of cases involving the General Assembly and various "special rapporteurs" an impotent talking shop, so the ruling was comprehensively ignored.
The UK receives many derisory letters from UN special rapporteurs, for example from Philip Alston in 2019, Tendayi Achiume, also in 2019, and Olivier De Schutter in 2023. The majority of these are ignored by the UK government, and this latest one seems to be no different. The main difference so far appears to be that the letter has been both requested by and promoted by Just Stop Oil because it supports the group's members who have committed criminal offences obtaining special treatment from the court system.