Information is the key: you need to find out why exactly your application has been rejected. Information will help you find out what you need to do next time to sort out the issue, and if there is something specific then it could be easy to resolve.
Don't fall into the trap that many do of thinking that if their application is rejected by one mortgage lender then all will follow suit - because the criteria from one mortgage to another, nevermind from one provider to another, can vary dramatically, so it could be that what you fall foul of won't be an issue with another type of mortgage or with another lender. But seeking a reason as to why it was rejected is the key as that information is what you need to make progress and apply, hopefully successfully, next time around.
If there are problems with the credit checking, and you don't think these are correct, then you may need to get hold of a copy of your credit rating to see what is there and to potentially dispute any issues. If it is simply a case of not reaching certain agreed criteria then you need to find out how to meet those criteria and take active steps to do so.
Remember also that there may be a difference between the best deals out there on the market and the ones that you can actually afford to take out. It may be that in applying for the most attractive mortgage you are actually reducing your chances of getting accepted, so do consider all options when it comes to getting a mortgage.
Ultimately, it may be the case that you need to wait a little longer to be approved, for instance you simply need to have more capital to your name and if you don't have the necessary savings in place or if you simply don't earn enough to meet the multiplier, then there is nothing you can do other than remain patient for a little bit longer, but in many cases that isn't the situation so it pays to find out why you are being refused and then applying to alternative lenders rather than simply giving up.
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