We visited Place in the Sun in Birmingham, last summer, to bring us up to speed on questions we needed answering. One which we forgot to ask was, 'does the tax office, in Portugal, take 40% of your pension'?
I have 2 accountants one in the UK and one here in Portugal. I declare my private pension to The Portuguese IRS and it is tax free up to a limit of about 8/9000 euros if you can prove it is an annuity. I am sure that someone on this forum has more up to date figures than I have.
When you receive your state pension in the UK you have to pay tax on that if you go over your UK allowances.
So in a nutshell I pay UK taxes on income in the UK and Portuguese taxes on income in Portugal and have been doing this for almost the last 4 years. The inland revenue are happy and so are the Portuguese IRS.
So to answer your question the first lump is tax free and then the rest depends on the size of your pension.
You can opt to pay all your taxes in Portugal, HMRC have a form to be completed, as a Resident you should make a yearly IRS (Tax Return) the the exception is if your world wide income is below taxable levels.
Certain UK pensions can only be taxed in UK, but if this is the case or you opt for UK Tax then they should be declared and the tax paid.
IRS Tax return is taken as a family unit, separate forms for certain items but combined forms for most things like claiming % health, dental, optical etc.
A lot depends on your pension and other income but it can be beneficial to declare and pay 100% of taxes in Portugal, and no they don't take 40% of your pension unless your pensions/earnings