No, 0345 numbers are not completely free to call from any EE phone in the UK, however they are compatible with inclusive free minutes allowances so if you have spare free minutes on your EE phone then you can call any 01, 02 or 03 number, including any 0345 number, effectively for free until your free minutes allowance expires.
What are 0345 numbers?
0345 numbers are non-geographic telephone numbers (in the UK at least) which follow the rules of all 03 numbers whereby they are charged at an identical rate to 01 and 02 (geographic) numbers.
Why are 0345 numbers so popular?
0345 numbers are so popular since 2015 because 0845 numbers were so popular before 2015 and due to Ofcom’s new regulations that came into force on 1st June 2015 all UK companies’ post-sales customer service helplines must avoid using 0845 numbers. 0345 numbers exist as a replacement to 0845 numbers which are now illegal in the United Kingdom for use as after-sales customer service helpline numbers. The new regulations specifically state that after-sales customer services must be accessible at standard rate or cheaper (permitting the use of 01, 02, 03 and freephone numbers only).