There really is no need either. Early access to poll results and crosstab data excluded from public results is still extremely valuable.
Out of genuine curiosity (I'm American and don't know all the workings of UK government), is the public actually paying for these polls (via some agency in charge of that)? If so then yeah, "the public" is a client and if they were getting shorted in favor of private clients against the contract then that'd be a problem.
On the other hand though if polling companies are just doing it as a public service or form of advertisement (aka "see how accurate our public polls are on general elections, you can also expect that kind of rigor if you pay for us to poll about your product") then I'm not sure what the public interest angle is in terms of "less accurate public polls", nor do I see an enforcement angle given that those could just be the normal cheaper ones the company does and it's private entities commissioning and paying for more extensive, expensive and accurate collection. As far as I know polling companies themselves are private entities and are just offering a service. And in practice my understanding is that a lot of "public polling" is specifically being paid for by private entities in the form of newspapers and the like that then release it, because it sells news and in turn the ads attached to them. So same thing, if the news organizations found out they were being screwed they'd sue, and if results are bad enough they won't go with that polling company again, it's a competitive area.
If the public isn't paying though then I don't see what else can be expected?