Hi he will be worse off as even a very small pension such as seeps possibly say £3 per week will place a bar on receiving pension credit.
Yes you can claim yourself for certain benefits in part but you miss out on things like free boilers, insulation, £140 fuel grant, free parking discs, soon over 75's TV licence, the list goes on, I actually complained to my MP who took it up at Parlimently level but the dosy lot could not understand that I was worse off, rant over.
Please be very careful about the information put forward as fact. £3 added to a basic state pension does not stop you claiming some of the things you have listed. The £140 Warm Home discount is provided by the energy companies - not the government. They have are given a list of "core" claimants who get it automatically. This includes those on Pension Credit. Others fall into what they call the "broader" group. You need to apply in September for this as it is on a first come first serve basis. They will take into account your income and what percentage of that is going on fuel. They will also take into account your health and mobility. It's a pain but you can still get it.
As far as I am aware free boilers and insulation are no longer available. Some companies offer what sounds like a grant for new windows but it is basically a discount and I believe they have been told to stop the way they sell this.
Parking discs for free parking surely only go to those who are disabled? If you are still disabled you will still be able to get one. There is no relevance to income only to your mobility or other health factors.
There is a separate method of getting help with dental costs which seems on the face of it slightly more generous than other applications. But the application form is truly horrendous, pages and pages, and complicated. I gave up on it and dug out a credit card instead.
If you are really counting every penny you learn how to fill them in or get someone - Age Concern are good - to help you. If you are filling in a lot of these forms it does become easier.
I did post about the different ways they assess what you pay for care on another thread - everyone pays which is not always made clear - unfortunately, it was not published
but I think that is the most complex system I have come across.