Because Companies House has woken up to the identity fraud problem of lots of personal info in the public domain … If he moves out you cannot get those Companies House addresses changed easily (except maybe with a court order) without his cooperation.
IMO if he is a risk of default in the future you need to get him to do it and now. If you have to evict him it will be an even bigger nightmare.
As for the two directors who I assume are not living there they have no business using your address as a service address without your consent. They have no legal connection to that address and I’d argue no legitimate argument for being registered there.
If it were me I would say that I wouldn’t even contemplate renewing / the application until that was all done and the registered office and directors were all moved to an appropriate location (a registered office/service address service is provided quite cheaply by many smaller accounting and legal firms). For suppliers it’s a bit different as he needs to get invoices so as a trading address personally I might be more flexible (but it’s not my house here).
I would also get the tenancy agreement to explicitly exclude any other person using that address for business correspondence.
We moved into a property that a self employed business (that was still running) had been run from and it was about 3 years before all the supplier post stopped. It took at least a year for the final deliveries to stop. Luckily our vendor was helpful as it was impacting him.
IANAL.
@mashr if it’s small scale mobile hull cleaning services there will be plenty of less than wealthy boaters using those. The marine industry has never been known for its economic stability.