The situation is common, the solution is NOT simple.
You are confusing succession and tax. The UK has no jurisdiction over taxing your wife as she is not domiciled here - if she were her entire world wide estate would be subject to UK inheritance tax, and that would probably not be desirable. However theoretically there is no pronblem with applying "British" succession rules to her assets in the Philippines - this would presumably mean she has complete testamentary freedom and can leave them to whomsoever she wishes.
One problem though, there is no such thing as "british" law. You say she is of British nationality (I assume born in Egypt to British parents) but the applicable law is either England & Wales, or Scotland, or Nrothern Ireland, beacuse of the three legal jurisdictions we have in this country.
The doctrine of renvoi may well bounce the issue back to the Philippine courts, but if they refuse jurisiction then the situation would be saved by "UK" law in some way, but you would need to seek expert advice.
Richard Frimston at Russell-Cooke Solicitors in London is probably the most high profile exponent of this area of international law. You will be able to find his details on their website,
www.russell-cooke.co.uk.