"Right, so I have to plug it into the BT broadband thing then."
Yes.
"Then when we are away on holiday or switch the system down the phone doesnt work?"
Yes again, the same when you're on holiday. However... The VOIP provider will "know" when your phone is off and they therefore could, in theory, provide an answer phone service. It looks like sipgate do this, but I don't really know enough about their service to comment in any detail. You'd have to check their web site or speak to them.
"When you say VOIP service and phone number, does that include a BT number and BT broadband then?"
No... By that what was meant that a company like sipgate would give you some details that you would enter into your phone. I'd expect it to be an address (sip gate.co.uk:12345/voip/myphone) an account name and a password. You might be able to enter those details straight into the phone. Or with your phone plugged into your BT router at the same time as your computer you would go to some special web page and enter the details.
"So what are the advantages of this then?"
In theory it can be free, you can have multiple phone lines working off the same broadband connection and it can work even when your phone is turned off. You could even move the phone around and still be reached on the same phone number, or you might be able to get at your calls when your away somewhere using a computer or another phone. So it's a bit like a mobile phone, it doesn't "have" to be plugged into one place in order to work.
But given your situation I can't help but wonder if a normal phone and answer phone would have been simpler.
"My problem is we are rural and our telephone line with cordless is very faint and been told I need a corded system."
I hope your broadband is good enough then... If not the calls might cut out or sound awful...
"Does this mean our calls are free?"
Have a look at the call rates page on their web site...
Calls to other sipgate and VOIP numbers are free.
However there are charges for calling "normal" UK phone numbers. At a quick glance they seem cheaper than BT day rates and bit more expensive than their out of hours rates. But again have a look, you might be on some different BT contract.