Might be wrong but this kind of reads like you haven't actually invoiced them and are reliant on the contract between you.
That doesn't prevent you from raising an invoice as soon as the job is done and billable in future, id suggest you do that so that you at least have a date at which you can say the 30 day clock is ticking.
I'm pretty sure you can't charge interest unless it was already in your terms and conditions. Again, I may be wrong, but the only suppliers that have raised the threat of interest have it clearly marked in t and C's. I'd tread carefully over billing them that as it may just slow your main payment.
I don't freelance, but I do pay supplier invoices. 10 days isn't even considered "late" by most accountants responsible for making payments, so not unusual. Even in large businesses there will only be one or two payment runs per month (it's not practical to pay invoices every day) so if you just missed the last one sometimes there is quite a wait for the next one.
These large online media companies have a lot of presence online but probably have a pretty small accounts department.
It may not even be the accounts depts fault, they are likely waiting for the department that commissioned your work to say "ok to pay"
Above probably Doesn't really help you, but this does sound a fairly "normal delay".from your own planning perspective, I think it's best to get into the mindset that you would like to be paid in 30 days but to assume you will actually get paid in 45-60. Might be painful for a few months, but will save you a lot of stress in the long run.
There are means of pressuring it further, small claims court, debtor recovery letters, but imo they are only justified for 3 months or older debt, anything less is usual course of business.
In my experience the bad payers (i.e slow but they do always pay) are often the best customers in every other respect, so it's a rough with the smooth thing.