This is a very complex issue that varies from case to case. In general, to minimise the risk of refusal, it is certainly worth looking into the distinctiveness of your mark and searching existing marks whose owners could oppose your application. Trama offers both of these checks in its free lawyer's check.
Other general advice might include opting for a logo trademark instead of a wordmark, as a logo with multiple distinct elements is more likely to go through. Figurative marks are generally easier to distinguish than wordmarks, mainly due to the limited number of words and their combinations that are becoming more and more numerous in trademark registries.
Also, always make sure that you avoid using prohibited elements such as flags, signs, names of the Royal family in the UK, etc. We recommend checking prohibited elements in each jurisdiction individually, as they might differ.