What they need is to be able to search on a couple of platforms and maybe find a private account and one with a few innocuous follows. No accounts creates suspicion, as does something set up in the last month. It never hurts to follow Gardeners' World, Springwatch and The Archers, either - I reckon the majority of their follows under the age of 55 are for the purposes of pre-employment searches - bung in some non-controversial music, maybe a couple of things linked to something you've mentioned in the applications and that's made things pretty non descript.
Make sure none of them are linked to the same email address as you've made applications from - I whistleblew once and it was only because I'd used the same throwaway email address for a throwaway account for competitions that I found an involved party started following that account within five days of the disclosure being made, which meant they'd used the 'find people to follow' option.
Make sure there is nothing contentious still visible on the ones you can't actually delete/are linked to you IRL and you can't change the name on (FB will have your original name visible, for example).
Check your friends' tagging and posts to you - it's easy to go from looking at one account, click on the friends' link and then there's something really stupid on there that makes you look bad by association.
Never have friends of friends as an acceptable security level. There is always somebody able to get through that way.
Obviously, if it's government related, none of that matters and they'll see everything, but for a bog standard check, it should be enough to cleanse things for an overworked person in HR to just type in a username, think 'nothing to see here...nope, nothing there, either' and then move on to the next job on their to-do list.