Best judgement: lack of information
You may encounter difficulty when trying to make an assessment to best judgement.
If a business is unable or unwilling to provide all the information you would like or has not kept comprehensive records, you would be fully justified in raising an assessment.
This may include higher range estimates, see Spillane v HMC&E 1990 STC 212.
If the amount of the assessment is disputed then the onus is on the business to disprove the assessment, perhaps by providing further information or reconstructing its records.
In the Van Boeckel case the High Court held that although HMRC had to exercise their judgement as to the amount of the assessment in a reasonable manner, they were under no obligation to do the work of the taxpayer by carrying out exhaustive investigations.
In a colourful analysis on the same theme, the High Court in the Schlumberger Inland Services Inc.  STC 228 case considered that, where a business provides only the minimum of information to HMRC, the officer raising the assessment
is not required to possess and deploy the deductive powers of Sherlock Holmes and the clairvoyance of Madam Arcarti provided that the assessment raised is not in excess of what could reasonably be payable.
Therefore where a revenue trader fails to keep comprehensive records or is unable or unwilling to provide all the information we require, an officer would be fully justified in making an assessment based on the information available.
Clearly, the accuracy of the assessment will suffer from the absence of complete information but this is acceptable, as long as the best judgement assessment is fair and reasonable.
It is not the responsibility of the officer to reconstruct absent records or to seek records that are unavailable. It is the responsibility of the trader to provide this information. If traders dispute the amount of assessments so raised, it is their responsibility to provide more information or reconstruct their records as appropriate.