We maintain there is no confusion between our consumer-facing TV service, YouView, and the business-to-business billing platform, Yourview, provided by Total Ltd.
This strikes me as perfectly reasonable. If YourView is b2b, how would YouView users even know it exists? Is YourView worried that their user base-- whether existing or potential-- will think they've diversified, with ensuing loss of quality?
The essence of a trademark is that it applies to similar areas of business. For comparison purposes, look up some well-known name like "zipper". There are hundreds of 'em.
Raise your hand if you saw the subject header and thought the stink had been raised by YouTube on grounds of vaguely similar sound.