I think in the UK - GP's are quite open to these things compared to what we normally hear from the US. Don't overthink it, but be prepared. Mostly the NHS hates to spend money so they pull a lot of tricks to stop this happening like asking people to be 30 and so on.

Read This - NHS Female Sterilisation

Be prepared for these topics -
How long have you wanted this?
What are the chances you'd change your mind?
If you fell madly in love, and your partner wanted a baby would you have one?

Worth Remembering -
Your GP may recommend counselling before referring you for sterilisation
Your GP can refuse to carry out the procedure or refuse to refer you for it if they do not believe it's in your best interests.
If the GP agrees with your decision, they'll refer you to a gynaecologist for treatment at your nearest NHS hospital.
You'll need to use contraception until the day of the operation and right up until your next period after surgery if you're having your fallopian tubes blocked.
Sterilisation can be performed at any stage in your menstrual cycle