Upvote:2
Gov.uk advice for visa-free entry is to bring the same documents https://www.gov.uk/government/publications/visitor-visa-guide-to-supporting-documents you’d need to apply for a visa, to show to officers at the UK border. These should demonstrate, if asked, that you are genuine visitors per Immigration Rules, specifically V 4.2(b) “will not live in the UK for extended periods through frequent or successive visits, or make the UK their main home” https://www.gov.uk/guidance/immigration-rules/immigration-rules-appendix-v-visitor-rules The typical advice is to spend at least the same amount of time outside the UK as in it. The pattern of visits you’re describing is possibly pushing this, IMHO, so it may well be best to expect to be questioned on arrival and prepare accordingly. On the other hand, after a gap of 9 months you might sail through - it’s impossible to say.