If you are going away for one night in the UK, you do not need a travel wallet or flask. Insulin can be kept at room temperature for 30 days.
I was going to say that the case your insulin pen comes in is fine for travel. However, it seems to be common to prescribe single use pens which just come in boxes of 5. If this is the case, you can carry your pen in a pencil case. And I recommend requesting reusable pens when you next speak to your DSN. They are more robust, the cartridges take up less space in your fridge (and luggage when travelling), you can dose half units with them, some have a reminder on the end for how much insulin you have taken and they produces less waste so better for the environment. They also come in nice cases.
But back to needing a travel wallet, you don’t.