Can I call my company London Production House if there is already a London Films trading and doing the same work as we plan to do.?

You can, as long as nobody else in the same business with a similar name successfully challenges you. 

When you’re in the same business with a similar name, or use a different name but with a similar logo, you can be challenged for “passing off” your business (basically, impersonation).

You’ll be at lower risk of that happening if you maybe chose “Production House London” or “Production House (London)”.

But it’s certainly not unreasonable for any London based business to use that word in their company name, so it’s also reasonable to argue that “London Production House” and “London Films” are totally different names even if in the same business as rivals. Just look at all the butchery companies around London’s Smithfield Market which have “Smithfield” in their names.

Ultimately, you need the advice of a law firm specialising in corporate law and intellectual property law if you want to get an expertly informed opinion to minimise your risk of a legal challenge.

I would say yes, if no-one else has that exact name.

Check for any copyright infringement, possibly with Companies House.

sounds like something a Tosser would do 

Of course you can. There are thousands of companies with "London" in their name.

There is a bathroom supplies company called Victoria Plum. And another called Victorian Plumbing.

Whatever it is I am sure of it. 

You can.  They may sue you if they have that name protected.

There isn't a special legal structure for a film company is my point. ... It's so easy to do now, but if you need advice, why not choose one of the short ... Take your business plan to one of the big production companies, or even a studio. ... gear, you will start getting swamped with work, and you will need help.