the 2 i found are called:
'apollo cleaning (kent) ltd'
'apollo cleaning services ltd'
if i've got this right, being ltd as dave said will not give you anymore rights, the privite company thats contacted you are simply a company that makes its own register, and any of us can use them the idea is to protect your company name if a company pops up using your name, in your area, then this company will take legal action for you, the cost of which will be covered in your membership fee. (i think around £150 a year)
being 'limited registered company' is irrelevent, though it will prove how long they been using the name.
its who was trading first, what areas covered, therefore them being a national company, if they are? will have a bearing, i think they would also have to prove you have caused problems to effect in some way there trading.
theres lots of cleaning apollos, 2 are ltd, then theres the ones we dont know about.