I've not signed my contract of employment and am now five weeks into my new job

[Crazyindiechick]

Bizarrely I've now been offered another job. Same salary except wfh 2 days a week (rather than 4) and I'm not going to be managing anyone.
I've not signed my contract so do I still assume I need to give a weeks' notice rather than just a day (which is on my contract until I'm here longer than a month)

You may not have signed but you've not protested the terms formally and you have worked and abided by them. So the terms will apply, regardless of signature. So you should abide by the notice terms in them.

I'm not a lawyer, but was a trade union rep for a long time and that's my understanding of employment contract law.

By commencing & continuing work you have agreed to the terms.

I think if you want out - the union rep above is correct - but i suspect most employers would accept a ‘it’s really not working out for me here’ chat and a quick departure on good mutual terms.

I agree with this, it's worth having a conversation with them.

Thanks. I've not decided whether to take the new job yet!