With a few exceptions (absolutely terrible credit), most banks will let you borrow up to the exact amount of equity that you have in your home, because they are securing your loan against this value. In other words, because banks know they can get all of their money back if they sell your home and your home's equity, they have no problems letting you borrow up to that equity if the situation warrants it. (of course, if the housing market is falling, then banks may take a ifferent view and you maybe restricted by them.)
That said, if you are wondering how much to borrow, there is another question you should ask yourself:
Do You Want To Borrow Against Every Pound of your Equity?
That is a different question. If you know you can afford to make payments without any issue, guaranteed, then yes, you may want to borrow against every bit of your equity. However, if you think there is any chance - however small - that you will not be able to make one of your payments, then no you do not want to borrow against all of your equity. You want to leave a little bit of leeway, because if the housing market crashes, or continues to crash, then your home may lose value and lose equity, resulting in what is known as "negative equity."
Negative equity is when the value of your home is less than your home loan. That means that if you default on your home and it gets repossessed, when it is sold it will not cover all of the money you owe, and there is a chance that you will continue to owe money even after your house has been taken from you. Negative equity is a terrible experience. If you do not borrow against all of your equity, it is much more difficult to find yourself in negative equity. Negative equity is not as big a deal, however, when you can afford to make all your payments without question. But if defaulting is something that you think may happen, either because your budget is already strapped or you think you may be losing or leaving your job in the near future, you may not want to take out all of your equity in your secured loan .