Connecting wires - use a terminal block?

Hi, Been there.....
You should check out Wago and similar connectors. They are cheap, simple, and very effective. They also accommodate wires of different sizes all in the same connector.
There are spring-loaded versions that you can insert remove at will and more permanent pushwire types. Go for the spring type. they work about about 60p each for 5-way connectors.
If it were me, I would check out toolstation.com and see (for example) product code 68406
But there are many types, so you can review and select what works for you.