Organisations can in practice be fined up to 4% of annual global turnover for breaching GDPR or €20 Million. This is the maximum fine that can be imposed for the most serious infringements e.g.not having sufficient customer consent to process data or violating the core of Privacy by Design concepts.
There is a tiered approach to fines e.g. a company can be fined 2% for not having their records in order (article 28), not notifying the supervising authority and data subject about a breach or not conducting impact assessment. It is important to note that these rules apply to both controllers and processors – meaning ‘clouds’ are not exempt from GDPR enforcement.
How these fines would be enforced in reality for schools, LAs or MATS is to be seen, however, don't take the ICO for granted after their recent fines to BA and Marriott.