You would need an emergency fund of

£0

Why is Having an Emergency Fund so Important?

Having an emergency fund may not sound exciting, but it’s one of the most important things you can do to protect yourself from financial hardship.
The amount you should be saving in your emergency fund really depends on what type of emergencies you’re expecting, your current financial situation, and your goals for the future. There isn’t an exact amount that is right for everyone, but a good rule of thumb is to have at least three to six months worth of expenses saved in your fund.