Yep it's mostly down to the other power company.
I signed up to EK last Friday, gave them payment details Saturday. They told me Flick had told them they'd have me moved over "on or before the 20th June", but I'm still waiting. Not unexpected, and still within the ten day limit.
I got the same email and the same date of 20 June, and the email arrived on 20 June! Lodged the transfer request on the same day as timmay, and also still waiting.
That other companies can have their @#@#$ together and get transfers confirmed within a day or so shows it can be done, so a pity Flick isn't more on to it. [Edit: noting the comment above re Flick struggling; still, I'd suggest it can also be useful to send customers in this position an email to notify them of this - while I know it's within the 10 days, it can still head off people pestering them for answers and also be good PR to keep people in the loop.]
Is it 10 days or 10 working days?