You can be paid off but you have to sign a compromise agreement basically saying you agree not to take legal action. For it to be valid however you HAVE to take legal advice before signing it. This is the law. Thus, cashing the cheque doesn't signify acceptance. However, if you have verbally said you won't pursue anything that you have to think about the moral argument.
As to whether you'd get more than �1,000 from them depends on why you were unfairly dismissed and what the tribunal thinks. Bear in mind to go to court though costs time and money so consider that before deciding whether to pursue this. You're also unlikely to get a reference in from them if it goes this way and any future employer might look unfavourably at a candidate who was in legal action against a former employer.