Except for a few special cases, a ticket to London Terminals is only valid until you reach your first of the London Terminals. It is almost never valid by tube.
As explained on the National Rail Enquiries website in the London Terminals section
Tickets issued for travel to/from London usually show ‘London Terminals’ as the destination/origin rather than naming a specific station. This is because the ticket is valid to more than one London Terminal station provided it’s on any reasonable line of route. Tickets can only be used on National Rail services. For example, a ticket from Brighton to London Terminals is valid to Victoria, Waterloo (changing at Clapham Junction), London Bridge, Blackfriars and City Thameslink or Charing Cross Waterloo East or Cannon Street (changing at London Bridge). It would not be valid to, for example, London Euston or Paddington as this would not be on the line of route and would involve crossing London using another mode of transport.
If you want to get from Reading (or further west) to London Bridge on a London Terminals ticket, going via Paddington is not allowed. To go Reading – Paddington – London Bridge, you need to buy a ticket to London Zone U1, eg this Reading ticket, which includes the onwards tube journey.
Alternately, if you’re determined to get yourself to London Bridge on your current ticket… You can route yourself on the Reading to Waterloo train, and change at either Clapham Junction, or (post-August) Waterloo + Waterloo East. Either way it’ll be a lot lot slower, but your ticket would be valid via this slow route to London Bridge.
Credit:stackoverflow.com‘