I want to travel between Birmingham and Gatwick Airport, but need to make a 4-day stopover in Reading. Is there a train ticket covering this journey, or do I have to buy two tickets? Birmingham to Reading, and then Reading to Gatwick Airport)
Summary: You will need two separate tickets for this particular journey.
The National Rail Enquiries website gives the following description when introducing the Anytime tickets, the most flexible single journey ticket available:
Buy any time, travel any time.
What are Anytime tickets? Anytime fares are fully flexible tickets, with no time restrictions on when you can travel. Perfect for people who need complete flexibility.
You can buy Anytime tickets any time before you travel and you can use your ticket to travel on any train. With an Anytime ticket you can also break your journey at stations along the route of travel.
When can I use an Anytime ticket? Anytime Day (Single and Return) tickets must be used on the date shown on your ticket and up to 04:29 the following day.
Anytime Single must be used within 2 days of the date shown on the ticket and up until 04:29 after the last day of validity.
Given you are staying in Reading for four days, and not returning to Birmingham but heading to Gatwick Airport, you cannot use an Anytime Single ticket.
Since this is the most flexible single journey ticket available and it is still not valid for your case, you will need two separate tickets, one between Birmingham and Reading, and another one between Reading and Gatwick Airport.
Technically, there are tickets that cover such journey (e.g. season tickets, rover tickets), but they are very unlikely to be economical. Moreover, if you know which train you are going to catch, buying two Advance Single tickets might work out cheaper than one Anytime/Off-peak ticket (if that exist at all).