I can see what you are saying MOnica but what do you raise it to? I found the list of the "maximum" that people can receive really thought provoking - and not just in a "we want more because they get it" way but simply in a this is the most and that is received by the poorest.
So, the first thing to work out is where you would set Pension Credit level to do away with the need for the "bits and pieces". When looking at a Basic Income policy people often use the Personal Tax allowance. As the figures I gave for "other countries" were 2018/19 the PTA for this year was £11,500. I have my concerns that that is enough to live on AND pay for all the things covered by other benefits including Council Tax Benefit and Housing Benefit. You would need a generally lower amount if CTB became a local income tax. The French, as we saw, pay a maximum of £15,808. That might encompass CTB. I am a great believer in paying your council tax rather than having a benefit, even if it is paid to you by one hand and taken by the other. It is very undemocratic if people become unaware of what everyone else is paying. To encompass housing I think you would have to go up into the range of Spain and Germany, i.e., £26,676 to £26,364. It may be interesting to note that the cap on Universal Credit for a single person without children (which includes CTB and HB) is £13,400.
Let's say we chose one of these - let's go for £13,400 for the sake of argument. You would then, de facto have a semi-means tested pension. Anyone not claiming, whatever their income, would get the base rate. On the old pension (pre 2016) this would be £6,550.44 p.a., and on the new one it would be £8,546.20. Is this what you were thinking? I am not sure where the money would come from to pay for all the rise in Pension Credit - a great deal from not having to pay other benefits of course, but I have a feeling the base rates would begin to be frozen but possible not until the new Workplace pension starts to pay out and I am not sure if older workers are paying in to that.
By the way, nice to have a proper discussion about what might be possible.