How do I word this email?

[Whataroyalannoyance]

Hi, I took a new job, worked it for 4 days and realised that it was not going to be anything like the job I was sold ( much longer hours about 20% more than advertised with no pay for the overtime, person meant to train me had already moved to their new position, they decided that a licence that I had that they wanted wasn't from a company that they would recognise so wanted me to re do it etc) I spoke with them and expressed my concerns and said I didn't think it would work. Told them I was happy to carry on while they found someone else if they would be stuck etc. They said not to bother. How to I approach them about pay for the time I did work?

Did you sign a contract, and if so, does it say what the notice period is?

no, no contract yet, they outsource their HR so it hadnt come through.

Is there an hr or payroll department.

Apparently they outsource hr. The contact details (email) I have are for the person who would be my direct supervisor / manager. Online there are no other emails than a central sales email address.
I was asked to interview on a Thursday, offered the job. Asked to start the following Monday (last week) worked m, t, w, t. I had filled in the hmrc declaration but had no other paperwork.

If they don't already have your bank details it's easier.

Dear X,

Further to our discussion/my discussion with Y on Xth September 2020, please find this email a formal notice of my resignation.

As I believe I have not already sent over my bank details, I attach these now below with respect to the days I have worked (Xth-Yth September). From my calculations I believe the total remuneration for these days will come to £XY, based on my salary of £ABC pro-rated.

It was a pleasure to meet all of you and I wish the company the best for the future.

Best wishes,

Xxx

• "Xxx" = name not kisses!!