So what generally happens if you decide to cancel the return flight?

The fare rules specified at the time of booking governs this. If you don't them the airline should be able to provide them.

Will have to check on this

nithing....you lose any ff credit....if you do it often, youcould be blacklisted....

why don't you post some details?....good luck...

Well there is a possibility that I may have to stay in London
but I won't know until after I get there. It was originally a family visit but now the family member I'm visiting has become ill and I may wish to stay for a while.

My two choices for carriers are BA and AC.

If I don't know what my return date will be what do I do when I'm already in London.

If you haven't yet booked a ticket, then you have two choices:

1. Book a flexible ticket that allows you to change the return date, and initially book the return journey for whatever date you guess you'll want to return.

2. Book two one-way tickets. Be warned that this may be quite expensive.

If you've already booked your ticket, you can probably (but not definitely) make changes to the return journey for an extra charge plus any difference in fare. The fare rules should specify whether this is possible.

How do you book a flexible ticket?

Airlines' own websites will often offer this. It's generally harder to find on third party websites. If you're stuck, a bricks-and-mortar travel agency can definitely book this for you.

A flexible ticket is usually a full fare ticket that allows changes with no penalty. On many airlines websites, look for "refundable" fares and then check the rules for that fare to see if you can make changes for free.

Thanks for the information-Is it correct that the flexible ticket costs way more than the non-refundable return ticket?

Usually yes.

Not only are fexible tickets more expensive, they can easily be more than twice low-cost tickets or twice two one-way tickets.

Your best bet may be to buy a regular low-cost round trip ticket for a return date that may work. In the event you cannot return on the purchased date, you can check wether the airline will allow you to change the return flight for a fee or lose the return portion and purchase a new ticket for the return. In that event, you might gamble and purchase a second round trip with the intent of just using the first half or purchase a one-way.

As noted above, airlines don't like you to purchase a round trip ticket with the intent of throwing the second portion out but a 1 or 2 time event will likely go unnoticed.

Buy the cheapest roundtrip ticket you can get from your preferred airline. If you can't make your return flight, call the airline and cancel the flight. Explain the situation and tell them you will call them back when you know when you can return. It usually costs about $250 to make the change, depending on the airline, but ask what the rules are before you buy the roundtrip ticket. Some airlines require that you book the new return flight at the same time that you cancel the original return while some will allow you to wait until you are sure.

This would also be my method, but the OP mentioned that BA was one of her preferred carriers for this trip. Be aware that many of the lowest fares on BA are not changeable at all, even with a fee. Read the T&C's of your ticket very carefully before you purchase it.

If you are really not sure of what you are doing and how to do it, and I am not being insulting when I say that, go into a traditional travel agency, they will be able to do a search with their computer reservation system to find the best airfare that will suit your purpose and they will be able explain the rules and penalties of the airfares to you.