I overstayed my youth mobility visa by 18 days, before returning home to NZ. It’s been 6 months and I want to return to the UK, just for a few weeks, as a tourist. I’m just nervous that I’ll get to the immigration desk and be refused entry because I overstayed my previous visa. Hope someone can give me some advice!
Unlike Tier 2 visas, Tier 5 Youth Mobility visas don't have a mandatory cooling off period. In principle you are free to come back as soon as you want. However, as this other excellent answer notes, returning to the UK soon after the end of your Tier 5 visas can be problematic. Even absent your overstay, the border officer might have some concerns about a return so soon after the end of your youth mobility visa. They may suspect that you are trying to build a life in the UK.
Per the immigration rules, since you overstayed for less than 30 days, you aren't subject to an automatic ban. However, an overstay will still be taken into account when the border officer is deciding whether to admit you. The overstay means that your credibility is damaged. Combined with the quick return after the end of your Tier 5 visa, and the best case scenario for you is an intensive grilling at the border. It might be best to put off this trip for a year or two.
You haven't said whether you are currently employed, or in education. If you are unemployed at the moment, you are at serious risk of being refused entry. UK border officers tend to think that the young and unemployed are at the biggest risk of overstaying (on the basis that this means there is nothing "tying" you to your home country).
If and when you decide to go ahead, you would be best advised to apply for a standard visit visa before returning to the UK, rather than relying on visa-free travel. Getting a visa refusal is far less uncomfortable than being refused entry. If you're unemployed, put off the trip until your circumstances change. It should go without saying, but you must disclose the full details of your previous visit on the application. The Home Office know you overstayed. If you try and hide it they will catch you.
If you do decide just to chance it at the border, bring lots of evidence of your employment/studies, a detailed itinerary, return tickets, and evidence of your healthy finances.