The return to work in a ‘hybrid’ model means that I may only be in the office 2 days a week. The way it’s working out with chaotic childcare plans and requirements is that I’d need a car just one of those days.

Is it possible to have a weekly, one day hire arrangement?

Bike and train and bike again are in the longer term plan.

Is there a local car club? you could see if their rules allowed you to have a regular booking

A few years ago my old workplace introduced a policy of all business trips not on the train had to use a hire car. This meant that once a week I had to hire a car, it was an absolute ball ache.
As I left early in the morning I had to collect the car the night before and leave work early to get to the hire company before they closed.
Collecting it was always a faff. No way would I want to rely on doing this before work. They didn’t offer a drop of service but would collect me from my house.
This wasn’t classed as long term rental even though it was pre-booked in advance for a few months.
If you aren’t travelling that far I’d honestly just look at how much a taxi will be.

Lift share, car club, taxi, public transport before hiring imo.

Pook later…

“I had to buy this VW camper van. I asked everywhere and there really wasn’t another option”

For ~47 hires a year it would need to really cheep to beat owning an older car.

£300 insurance
£150 tax
£50 MOT

Tyres etc are going to perish at that usage level before they wear out.

Even booking long in advance it’ll be £30-£40 /day Vs the £10/week owning a car would cost you.

That or find a lift share that’s doing the same route.

It’s certainly possible but I can’t imagine anywhere would do it cheaper than the normal day hire cost. If it really is chaotic, then taxi might be your better option – find a regular one with disabled access so you could take your bike with you & just do one way? Taxi is more likely to be amenable to regular 1 day per week discount too.

Taxi is more likely to be amenable to regular 1 day per week discount too.

IME no, their fares are set by the council.

Depending where you live and how far you need to travel, how about zipcar or similar?

Sounds like you’ve just described a taxi. Either that or bangernomics as TINAS said.

Do you have to go in, is it a requirement of your job?

IME no, their fares are set by the council.

Okay, private hire rather than taxi 🙄

Just arrange loads of 24 hour test drives with different car manufacturers :p