Hi there Angel,
Congratulations, your wife is now approaching the final step in her immigration journey.
Of course there is no legal requirement for her to obtain British Citizenship, but there are advantages. Not least when considering the ease with which overseas travel suddenly becomes without usual hassles relating to visa's
Now, when she is granted Citizenship she will also receive details of how to book and attend the British Citizenship ceremony and oath-taking.
That's where she will be presented with her naturalisation certificate. It's only at this point that British Citizenship is given.
From this point forward she will technically no longer be a Philippine citizen. Though of course she will still have her existing RP passport.
In order to become a member of that exclusive club of Dual Citizens, she will need to re-acquire her Philippine Citizenship. This is very easily and quickly achieved at a simple but very nice oath-taking ceremony at the Philippine Embassy in London. She will of course be presented with a very nice Certificate proclaiming her rights as a Philippine Citizen.
These days the Embassy is located in a very nice part of Picadilly, close to the tube stations and, dare I mention, shops.
To be a true dual citizen you need British Citizenship first. The Philippine authorities determined that in these cases your oath and alliegence to the Phils must be the most recent ceremony.
Those who have Dual Citizenship are legally entitled to hold two passports.
Be aware that when your wife attends the Philippine Embassy for her Oath Taking ceremony they will cancel her existing Philippine Passport and request her to apply for a new one.
I would suggest that she applies for and holds a British Passport before doing this just to cover for any delays in receiving her new Philippine passport in case overseas travel would become necessary.
When my wife applied we were not aware that her existing passport would be cancelled and we had a trip to Philippines planned for about 2 months later.
Anyway, a Philippine passport is not necessary to travel with and we cleared immigration with her British Passport, Philippine Citizen Certificate and our marriage certificate without any problems and still maintained Balikbayan Status.
Look here at the Philippine Embassy in London website for details of Dual Citizenship:-
Hope this helps