Fareham to london

The term you are looking for is "breaking your journey". I am assuming by an "open" ticket you are referring to an anytime ticket.

In the UK for anytime tickets you can break your journey. National rail notes that:

Break of journey

You may start, break and resume, or end your journey at any intermediate station along the route of travel.

So the next question - is Fareham to Reading to London a permitted route? You would not be allowed to say from Fareham to Inverness to London. So which routes are permitted? Where is the line drawn?

I am assuming you have an any permitted ticket without any restrictions, you can tell if your ticket has any restrictions by looking in the lower right and corner. Have a look at this which has restriction code FE. You can have a look at the meaning of a restriction code by going to http://www.nationalrail.co.uk/YOURCODE (so for the ticket above, http://www.nationalrail.co.uk/FE) and see if they apply.

But for tickets with no explicit routing restriction, where do we draw the line? If you have a look at the ATOC website then you will see your journey is equivalent to a Portsmouth Group to London Group ticket.

You can then have a look at this PDF (very large - 2,270 pages). You will find this line on page 1,555 and at the time of my writing it says:

BB+BL   CW+LB   CW+LF   PD   SW

You should interpret each cell as an or, but each "+" as an and. So you could use maps BB then BL, or just PD, etc.

You can see the maps on the ATOC website. The rules for how to follow the maps are:

1. Tracing must start at one of the ends of the route code.

2. All maps must be used.

3. Maps must be used in strict sequence, first to last or last to first, for a return journey.

4. Tracing may move from map to map only at a point where the two maps touch.

5. Once route tracing has left a map it cannot return to it.

6. Journeys may not double back except between stations which are members of a routeing point group for interchange or unless an easement permits it.

So lets have a look at what the maps mean in your case? I have done a (terrible) overlay of the BB (Blue) and BL (Red) maps to make this easier.

So we can see a route traveling from Fareham to Reading and then into Paddington while following the rules above. As such: yes, you can break your journey at any intermediate point, and you can travel via Reading on your ticket (assuming it is any permitted). Note that you need to follow the maps exactly, you cannot simply get any train, it must pass through (with or without stopping) the routes listed.

Just a quick additional note that the technology behind ticket barriers is quite old now and can have problems. Since there doesn't seem to be any reason why you would travel from Fareham to London this way (unless you wanted to stop off) then the ticket barriers at Reading may reject your ticket. I would leave more time then usual to arrive back at the station, and show your ticket to a member of staff instead of putting it through the barriers if at all possible.