https://www.southernwater.co.uk/Media/Default/PDFs/WaterSupplyRegs.pdf
Follow page 5 of this and you won't be far off. What I don't get is how you'll be able to put your double check valve and isolating valve inside if you can't find where this pipe comes from. A double check valve outside or incorporated into the tap isn't a very good solution as they tend to freeze and then you will experience poor flow and the double check valve probably isn't going to act as a check valve after this.
However, pragmatically, what you have is has probably been installed as a non-compliant outside tap in the past, so I'd be inclined to say that, as an amateur you are unlikely to have the skills to be able to trace this water pipe back to the origin and cut out and repipe from scratch.
As a replacement tap, you would be allowed to fit something like this as a replacement: Pegler HU Bib Tap with Check Valve ½. , but it needs to attach to a wallplate elbow, which you'll need to fit. The Water Regulations aren't retrospective, so you can work on existing systems provided your work makes them more, rather than less compliant.