Hi Stuart and welcome to the forum. Being a Brit you ought to know that nothing is ever straight forward when it come to dealing with the UK government. Firstly, you should be able to bring you kids anytime without a problem as you can register them at the British Embassy in Manila and apply for British passports for them if your name is on their birth certificates. Your wife on the other hand would require a visitor visa and that's not quite so simple.
The refusal rate for visitor visas is quite high. The usual reason for refusal is that they don't beleive she will return to the Philippines when the visa expires and the things that usually reassure them that she is more likely to return are property, money in the bank and regular employment in the Philippines.
The other route is a settlement visa which requires that you can house them and support them without recourse to public funds for a period of at least two years. A settlement visa application usually requires a lot of documentary proof of income, savings, housing, etc, etc before it would be granted
Iain