Full devolution of income tax to Scotland will not push it closer to independence because national insurance will remain a UK-wide tax, according to former chief secretary to the Treasury Sir Daniel Alexander.

The former Liberal Democrat minister suggested national insurance, which he acknowledged is a second form of income tax, will be one of the bonds that keeps the UK together as Scots will retain a sense that they are paying into UK services.

Speaking at the Lords Economic Affairs Committee, Sir Daniel also said that scrapping the Barnett Formula, which calculates Scotland's share of UK spending, would be "a waste of everyone's time, effort and emotional energy".

Baroness Wheatcroft asked Sir Daniel: "Do you agree with the position to devolve 100% of income tax?

"Isn't there a risk that emotionally, at least, that takes a step closer to independence rather than devolution?"

She questioned what ties Scotland would feel to reserved issues such as defence if 100% of their income tax is going to Holyrood.

Sir Daniel said: "I see the argument. I think my response would be that I am not so worried about that, because in the UK we actually have two forms of income tax: one is called income tax and the other is called national insurance, but they are both income taxes.

"Your national insurance goes entirely to the UK Government, and that is a contribution to what the UK Government does and that is paid by everybody, and your income tax goes to the Scottish Government.

"So given that we have two income taxes, one which is effectively going to be fully devolved and one which is fully reserved, I think to my mind that maintains the sense that everyone is making a contribution both to services in Scotland and services at a UK level."

Lord Kerr said the Barnett Formula - which allocates a higher share of spending-per-head to Scotland than other parts of the UK - "creates a genuine grievance for the Welsh".

He asked whether a needs-based system would be more appropriate.

Sir Daniel said: "The 2010 election on a Liberal Democrat manifesto proposed a needs-based assessment.

"I changed my view on that during my time in office because I think the process of moving from the Barnett Formula to some sort of needs-based assessment would be one that would be lengthy and rancorous and would result in an outcome that had broadly the same results in terms of financial allocations as the system that exists at the moment.

"That would be the nature of that sort of row, and I think that it would be a waste of everyone's time, effort and emotional energy."