There's not a straightforward answer to this from a legal perspective.
Andrue is correct to say that there is no implied term of fitness for purpose in relation to services - that only applies to goods.
There is a requirement that services supplied in the course of a business are supplied with reasonable care and skill (s. 13 Supply of Goods and Services Act 1982
), though showing unreasonable care and skill requires establishing the existence of a duty of care and a breach of that duty of care in the same way as in a negligence claim. Those matters are not something I can summarise in a forum post, not least because it may require some research to find any relevant case law.
Andrue is correct to point out that the redress available for mis-sold financial products relates to the regulated nature of those products. This satellite contract does not have any of those rights attached.
Stevenage_Neil has suggested the statements made about the service might be misrepresentation. I think those statements are more likely to be explicit terms of the contract rather than representations, though it depends on the precise details of the contract formation.
The problem I can see is that the statement about not over subscribing the service does not bind the provider to sticking with that decision in the future. It therefore seems a weak basis to argue for breach of contract.
I'd go to the core terms of the contract - a connection of up to a given speed, which implies a certain quality of service, when the true service is extremely slow. If the service is describes as 'broadband', that bolsters the case that the service contracted for has a minimum acceptable quality of service.
If an implied term about a minimum acceptable quality of service for the majority of time exists, it is likely to be what is known as an innominate term. Breach of an innominate term that deprives the innocent party of substantially the whole benefit of the contract gives the innocent party is entitled to terminate the contract (Hong Kong Fir Shipping v Kawasaki Kisen Kaisha
 2 QB 26).
You could bolster this claim by arguing that the argument that the s. 13 Supply of Goods and Services Act 1982 requirement to deliver the service with reasonable care and skill is not being met considering the repeated excuses for an unacceptable and unusable quality of service. In negotiations with a company, it is unlikely to matter that you have not demonstrated the existence of a duty of care and breach of that duty to the standard required in court. The term implied by s. 13 SGSA 1982 is also innominate, with the accompanying right to contract termination if the breach deprives the innocent party of substantially the whole benefit of the contract.
If there are exclusion or limitation clauses in the small print that appear to prevent this sort of claim, they are not necessarily operational. What exclusion clauses the provider can rely on is, again, not a straightforward matter of contract law.
As can be seen, suspected breaches contracts for services are rarely as clear cut as breaches of contract for supply of goods.