Each company needs to have a registered address. The company's address does not need to be one where it does business - just one where official mail and court papers etc can be delivered. It would not be unusual for a small company to use the address, say, of their accountant's offices.
However, UK Ltd reporting requirements also include the need to inform Companies House of the officer's details including:
name, service address, usual residential address, country of residence, nationality, and business occupation
So no, unless you are not an Officer of the company (director, secretary, etc) you can't avoid reporting it, and the Companies House records are open to the public.
From the Companies House website
Directors’ names and addresses are publicly available from Companies House. You can stop your address from appearing on the register if you or your family are at risk of abuse or harm because of your company’s work.
I doubt you would qualify for the exemption.
Tracking you down would not be difficult. If someone even suspected you were operating a company they can go to http://directors.findthecompany.co.uk/ and enter your name. It will pull up all the company information, including the company's registered address. That provides more than enough information for them to go to Companies House and get your home address.
I tried it and it pulled up information from a company I dissolved 20 years ago.