You need a 1/2 inch female x 1/2 inch male fitting. That will take the place of your nut and allow you to connect your tails.
You may need a washer or two that will act as a spacer or that fitting might tighten up against the worktop.
That photo is confusing as it looks like you are trying to join two flexi's ?
What do you have in your right hand that you will be fitting to the iso valve ?
It's 1/2 inch BSP...my fifty years tells me that. A 3/4 inch would have a bigger float.
Also , back in the day I would cut a washer down to fit what is needed here.
The good old 24 cdi's from the mid/late 90's.Fitted a 100 or more back in the day but probably time for a new boiler. These were non condensing boilers so you will need some alterations.
In post six you showed a picture of your hot & cold flexi hoses and they look completely different to each other.One will fit straight onto a flat faced iso valve and one has a male iron fitting.Did they come like that or have you altered the cold hose ?