There are a number of issues which are relevant to the question, without really answering what has been requested.
What is a British Company these days? Is it a Company based in Britain, or one that has the majority of its business interests in Britain, or even one that is registered on the UK stock exchange. I only make the points because the situation is not clear. Nissan builds cars in the north east and exports them back to Japan. The biggest owners of the US in Company terms are the Brits, although they 'hide' behind American names. Rolls Royce makes the 'worlds best cars' but is not British owned, but all manufacturing is done in the UK.
In a global economy national interests become very blurred. What I think is important is the effect that any business has on the way of life for the UK population, if it is beneficial then regardless of national identity, it should be welcomed. My daughetr works for ASDA and considers herself working for a 'British' Company, but as we all know ASDA is part of Walmart. Her salary is in Pounds, her pension is British ruled, her working conditions are British controlled, so where does that leave her, and all the others when considering what is, or is not British?
Conversely, British Airways is probably considered as being a totally Britsh Company. But without its revenues from working the global market, it would not survive, and in many countries where it does business it effects affiliation with local issues in order to be accepted. It has no choice.
Therefore without any disrespect to the question regarding 'Britishness' I suspect we have moved well beyond where that is even a question that is relevant to many of us. Like others I mourn the demise of the Empire, but it has gone and all we can do as individuals is take pride in our country of birth regardless of where, or to whom we gain our employment. The main export from these isles over generations has been people of value, and that is the one thing we can all be proud of, and should ensure is continued, regardless of the machinations of Blair and his cohorts.