I've been a contractor all my life (In the UK). I've literally never had a 'real job'.
Companies have always asked me to go permanent for them, and they've always tried to come up with reasons to do with intellectual property and long term loyalty.
And I've always said "OK, as long as you pay me the same". Which tends to end the conversation.
Just once in my whole life, that has also been the end of the contract, although even then the option was still open to become a permanent employee (at about half the amount they were paying me as a contractor). I think the company in question really needed to cut its budget.
Now I am old, a lot of my friends have gone into management. I've asked them why companies always try to get their contract staff to go permie. To a man they say "It's because it's much cheaper".
If the real reason was anything else, then they would be prepared to pay you more as a permanent employee than as a contractor. Because you'd be worth more to them.
It's just part of the negotiating game. Stick to your guns. If they can find someone of your quality willing to go permanent then they may replace you with him, and fair enough. But good people are thin on the ground, and the longer you've worked for them the harder it will be to replace you.
Unless they're about to go bust, if they find someone good, they'll employ him as well as you, because in any company that's not about to go bust, there's always more work than there are people to do it.
Since they've broken the ice and started talking about money, why not ask them for an extra £5/hour? Remember it's only a game. No one will take offence if you play too.
Also talk to some friendly purchasing people, or if you've got friends who are managers at other firms talk to them. They can explain how to play. In the worst case buy a book about negotiating. "Getting to Yes" is good, and a bit of a classic. Negotiating is great fun, and not at all the scary thing most people think it is.
And business is all about negotiation. If you negotiate well and in a friendly and decent manner, you'll get nothing but respect for it. If you play the game badly or spitefully, you'll just get classified with all the other clueless losers.
Honestly, if you play chess with someone and they keep losing their queen by making terrible moves, do you think 'Hey, he's loyal. I want him on my side?'