When I was checking mine, it was on the government pages, ministry of trade. There you get links for the trademarked names.
You can trademark a name for different areas. For example a country, Europe, or international! Of course the fees are accordingly.
For example a salon would only care to be trademarked within the country limits. I wouldn't care for example if there was a salon in Germany or Japan with the same name. But companies like CND are trademarked internationally.
As to the company's house that you mention, well I'd never heard of it. But as I said every country is different and there bound to be some restrictions.
We have a similar restriction here and truth be told, if there is an existing name I adopt, and neither is trademarked, then the owner of the original is allowed to sue me for the stealing. However everything is relevant again. If I have a restaurant in Athens called 'Steak House' and I was the first, then my main concern would be that no one else in Athens has the same name. But would I really care if I found such a restaurant in another city? No! Because there would be no competition. On the contrary, I might have suggested a partnership. Come up with same recipes for example or a common website. Point is even though I'd be the first on the government list, and the other restaurant wouldn't even be on it, I still wouldn't have any reason to doubt their name or their right to it.
But perhaps a UK based geek would be better suited to help you. I don't really know if it's obligatory for you to register.
The best advice I could give you is that if you are truly setting this up as a business then you follow business guidelines.
However, I get the feeling that you are looking at it all wrong. You are struggling with the legalities instead of enjoying the process.
A name is not something you pick out of a list, it's something that you get to live with for the rest of your life. Would you pick your baby's name out of a list?