If you have logged into the iplayer app, then BBC will have a record of it. They use a database of un-licenced addresses and also pull data from the iplayer log in page.
It would be difficult (not impossible) for them to prosecute without being able to evidence which programmes you actually watched.
The email is probably legit, and an electronic version of the letters they send to un-licenced addresses.
Just ignore it. It's computer generated.
BBC tv licence inspectors actually work for CAPITA BUSINESS SERVICES, they are minimum wage sales reps. They get £20 commission for every licence they sell, and £50 commission for every prosecution.
They have no legal powers. You do not have to give them the time of day. If you find one outside your front door, just ignore them. Literally. Do not get into any conversation and DO NOT sign the form they offer you. They will say something like
"Could you just sign this to say I have been here , it's so I don't have to come back again"
DO NOT SIGN ANYTHING!!!!!!!!!!!!
What they are giving you is a TVL178 form. It's the paperwork they use to submit to court to prosecute you and is an interview form. Once you sign it they will fill it out later and the questions you have "signed" will be used as evidence in court.
Do not believe the nieve posters who will state
"They're just people doing a job, they wouldn't do that"
They can, they will, and they have.
They are just salesmen. Do not speak to them. Ever.