Dropping out in week 3, do I need to include on UCAS?

I didn't do the in person registration but I did enrol online at the start of week 3

I don't dislike the course but I'd rather study somewhere closer to home in London

If I withdraw this week, would I need to include my attendance at the uni on UCAS? Would I be liable to pay tuition fees?

You need to list your full educational history on UCAS. Contact your unis finance department and ask when you become liable for tuition fees. Some unis allow you to withdraw within around three to four weeks from the start of the course without charging. If you are beyond your unis deadline, you will be liable for 25% of the annual tuition fee for this term. Do withdraw formally and inform SFE too. If you have been paid your maintenance loan, you will be required to pay back the portion that was intended to cover the rest of the term. If you have accommodation, you need to look closely at the cancellation terms - it is likely that you will be liable for the whole year.

Would it count as part of my education history if I haven't completed registration?

I feel like quitting a previous university course would hurt any future application.

I didn't do the in person registration but I did enrol online at the start of week 3
I don't dislike the course but I'd rather study somewhere closer to home in London
If I withdraw this week, would I need to include my attendance at the uni on UCAS? Would I be liable to pay tuition fees?

You need to speak to the current school so that the funding can be paid over to your new choice. Its vitally important not to ignore this and communicate your intentions so that they can support you with your move. No, you dont need to go through UCAS you just need to find the alternative University that has a placement and can enroll you direct or through what they call clearing if that window is still open.