Applying for the return of a rental deposit

[Ormally]

Has anyone done this recently for the end of a tenancy? The rental company says that we have to write to request it back. What should you include in that? Do we have to wait until the inventory check and results? Just hoping for any recent real life experiences.

Just contact the scheme its held in. If there's any dispute by the LL then the scheme will let you know what to do next

You have very substantial rights, assuming you are in England. I have never heard of you having to apply for it back. It should automatically be returned I think within 28 days of your departure, unless the landlord wants to request deductions. He needs to request those through the deposit scheme he is obliged to use, and you can then either agree to the deductions, or contest them.
For perspective: we were renting before we bought our current house seven years ago, and requested proof of the deposit being protected, which it legally has to be now for ASTs. The landlady claimed the agent was supposed to do it, and at the end of the tenancy, she refused to return the deposit because supposedly we had not paid a utility bill. The utility in question had a massive issue because we could not locate a supplier for the meter, and the National Grid said that the supply appeared to be illegal as it was not registered. So she had basically been skimming someone else's meter for years, and scamming each tenant out of their deposit as a result. Some of them got in touch with us to say she tried exactly the same thing on them.
Anyway, long story short, we sued her for 3x the entire deposit amount, using a no-win no-fee lawyer who took the case in five minutes. We won.

Read the guidelines: www.gov.uk/deposit-protection-schemes-and-landlords

When we left U.K. we just did one letter as written notice. Basically it said

We regret to inform you that we are ending the tenancy, for 123 High Street, Anytown, UK postcode and will be vacating the property on date DDMMMYYYY. Furthermore, we request return of the deposit in amount of £ pending inventory and inspection results to be deposited to the bank acct details. If the deposit is reduced, we request notification in writing specifying the cause and substantiating any costs charged.

We were on rolling month to month one at the time.

Mine was held by the deposit protection scheme, I had to apply online for it back. This was in July this year.

Thanks. Yes, whenever this has been done before, it's been automatic for me. The electricity tale worries me as we had a lot of issues for a few months when we moved in, as the former tenant seemed not to have completed with electricity readings and was being sent big bills (although the letting agents stipulate that they are supposed to send the final readings off to the supplier, and also we think that the property had been empty before the move in for a good while so potentially nobody would take responsibility for it). Will have a think.