It all depends on what you’re doing, where you’re going and for how long. Long haul flights are much more expensive than regional ones, for example, and insurance and visas vary country-by-country.
It's estimated that the average gap-year for young people is £5000, while that goes up to £6000 for more mature travellers and £9000 for career breakers, plus flights on top. The key word here is average, but it at least gives you a ‘ball park’ figure.
A gap needn’t break the bank, but it helps if you start by making yourself a list of all the things you might need to pay for, and then research how much it all comes to. Look at your chosen locations and do a bit of research as to how much the essentials cost – accommodation, food and travel, costs between towns/countries here. This will give you your absolute base budget per day, on top of which you can add costs for activities - seeing sights, adrenalin activities (if that’s your thing) and, of course, going out!
The gap-year guidebook includes a chapter on finance and insurance, which includes checklists of what you need to think about and expert advice. Here, you can search for companies that provide financial services.