Two ways to be lawful, and one way not to be
A small sewage discharge can be operated without a permit if it satisfies the binding rules — conditions about how and where it discharges, its capacity, its maintenance and its condition.
Where those conditions are not met, an environmental permit is required instead. Operating a system that meets neither is an offence carrying the prospect of a fine or imprisonment, which is a long way from the administrative problem most buyers assume they are dealing with.
The practical risk is rarely prosecution. It is the cost of being required to bring a non-compliant system up to standard, which can be substantial and which falls on whoever owns the property at the time.
Why your conveyancer will not tell you the answer
Because they have not seen the system and are not qualified to assess it. A conveyancer works from the documents, the seller's replies and the search results, none of which establishes the existence, location, condition or compliance of a tank buried in a field.
The Lexsure wording below says so in unusually direct terms, and it is worth reading as a statement of what the report does not cover rather than as a disclaimer to skim.
That means the compliance question is yours to answer, and the only way to answer it is to have someone look.
What to commission, and what to ask it to establish
An independent drainage engineer or environmental consultant, instructed before exchange. Ask them to inspect the system on site, confirm its type, age and location, assess compliance with the binding rules, and say whether an upgrade or replacement is needed and what it would cost.
Ask the seller in parallel: when the system was installed, when it was last emptied and by whom, whether it has ever been repaired, whether a permit has ever been held, and whether the discharge goes to ground or to a watercourse. Discharges to a watercourse are treated differently and more strictly.
Establish where the drainage field is and whether any of it is on land you are not buying. That is a rights problem as well as a drainage one, and it is a common and expensive discovery.