Build an emergency fund in small steps

Help me build an emergency fund.

My essential monthly costs: [rent, bills, food, travel, with a rough total]
What I have saved now: [amount, or "nothing yet"]
How steady my income is: [fixed salary, shifts that vary, self-employed]
Who depends on me: [just me, partner and two kids]
What I could put aside: [amount per week or month]

Ask me up to 3 short questions first if anything important is missing. Wait for my answers.

Then:
1. A first mini-target and a fuller target, with the thinking in plain words.
2. How long each will take at my saving rate.
3. Three ways to find the first small amount this month.
4. Simple rules for what counts as an emergency, and how to refill the fund after using it.
5. Point me to MoneyHelper for more on rainy-day savings if I want a second opinion.

Use only my figures. Don't recommend specific products. Only use what I've told you, leave blanks for anything I haven't given, and don't invent facts, figures or products. This is help organising my own numbers and wording, not financial advice; point me to MoneyHelper, GOV.UK or Citizens Advice for guidance, and to a free regulated debt adviser if I'm struggling to pay. UK English.

Stay in this ChatGPT chat. Do not turn on apps or connectors, and do not use memory from another chat.