As with most questions related to getting a mortgage or remortgaging, it really depends on your circumstances. Generally speaking, the more severe and more recent your credit issues are, the more difficult it will be. The level of equity you have will also play a role in this.
If you had a CCJ three years ago that is now satisfied, however, there’s a high chance that you will find it just as easy as someone with a perfect credit history to remortgage.