It all depends on what the fare is for the dates you wish to travel.

Being flexible does not necessarily mean it is in the most expensive fare basis. You could, for example, be booked currently in C class but there is only J class available on the new flight. in this case you will be up for difference between fare paid and J class for the return

Alternatively, stopovers may not be permitted in London - in which case a new fare which allows the stopover would be needed

Have you commenced travel yet?