What are you trying to accomplish? You hacked a site (probably not legal).You reach out and reported it (nice gesture). They fixed it (the site is more secure (yay!). They offered to pay you $1k pounds (awesome!). You are rejecting the offer based on lies you tell yourself (they can pay more and if rather share it with the world be cause good things will happen for me if I do).
Bad things can happen too. They can reach out to authorities. Your current or future employer could reach your future post and decide you aren't the right person for them. The underlying company could respond to your post and confirm you weren't authorized to test and a good portion of the security community would never seriously consider you for employment.
Sure, you might be able to negotiate a little more, if you take the right approach. How much do you want? 1200, 10,000, 50,000? When you do something wrong, even with good intentions, and now you aren't happy with the amount they graciously offered to compensate you with, your approach to publicly expose them if you don't get what you want because "they can pay more" seems less like they won't pay for my expertise and more like extortion.
When in doubt, choose the path you'd be proud to talk about in a courtroom.