Yeah they are allowed to do that if they actually suspect you are breaking the law like they turned up before and you were watching something but you didn't allow them in. But at the end of the day they are a private corporations acting on behalf of the BBC they don't have a right to look in your house than any other company does. If you remove the implied right of access they cant break in. Its kind of like installing a electric gate with a big hedge and your house being 1/2 mile from the gate. The gate wont open so therefore there is no implied right of access.

They also send weasel worded letter that heavily imply you are breaking the law when you are not and use super scammy psychological bs.