No, not exactly. 0333 numbers are not free to call on EE, they are charged at standard rate, the same as 01 and 02 (localised/geographic/landline) numbers.
However, if you have free inclusive minutes spare on your EE contract, you can rest assured than 0333 numbers are compatible with your free minutes, thus you can call 0333 numbers effectively for free until your free minutes allowance expires.
Why are 0333 numbers so popular?
0333 phone numbers only cropped up in recent years in the UK – their widespread use occurred in response to new Ofcom regulations which came into force on 1st June 2015 which made it illegal for companies in the UK to use after-sales customer service helplines beginning with 0843, 0844, 0845, 0870, etc. These service numbers are all charged at business-rate, generating a commission for the company you’re calling and they’re compatible with free minutes allowances issues by mobile phone companies like EE – therefore you would have ended up with a hefty phone bill for calling such numbers to complain about a product you’re unhappy with or to otherwise receive after-sales customer care for a product you’ve already paid for. This was naturally unfair, so the 03 number ranges were introduced as standard-rate, mobile-friendly non-geographic alternatives to the previously popular business-rate, mobile-unfriendly service numbers. 0300 numbers are reserved for government organisations and charities. 0344, 0345 and 0370 numbers mimick the traditional 0844, 0845 and 0870 numbers, to ensure companies’ heavily promoted customer service phone numbers remain memorable by matching their 08 equivalents. 0330 and 0333 numbers, meanwhile, are simply memorable numbers in their own right – ideal for quick-thinking companies to use as customer service helplines because they’re charged at standard rate (making them legal for post-sales customer care) and they’re new so the best patterns are not all already taken by other companies.